Search results for: Split Bregman Method

Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: Sari F. Alkhatib, Chang Je Park, Gyuhong Roh

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The iterative scheme which is used to treat buildup factors for stratified shields is being investigated here using the layer-splitting technique. A simple suggested formalism for the scheme based on the Kalos’ formula is introduced, based on which the implementation of the testing technique is carried out. The second layer in a double-layer shield was split into two equivalent layers and the scheme (with the suggested formalism) was implemented on the new “three-layer” shield configuration. The results of such manipulation on water-lead and water-iron shields combinations are presented here for 1 MeV photons. It was found that splitting the second layer introduces some deviation on the overall buildup factor value. This expected deviation appeared to be higher in the case of low Z layer followed by high Z. However, the overall performance of the iterative scheme showed a great consistency and strong coherence even with the introduced changes. The introduced layer-splitting testing technique shows the capability to be implemented in test the iterative scheme with a wide range of formalisms.

Keywords: buildup factor, iterative scheme, stratified shields, layer-splitting tecnique

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Authors: J. Hidalgo de Quintana, I. Stoner, M. Tackett, G. Doran, C. Rafferty, A. Windemuth, J. Tytell, D. Pregibon

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We have developed the Multiplexed Circulating microRNA assay that allows the detection of up to 68 microRNA targets per sample. The assay combines particle­based multiplexing, using patented Firefly hydrogel particles, with single­ step RT-PCR signal. Thus, the Circulating microRNA assay leverages PCR sensitivity while eliminating the need for separate reverse transcription reactions and mitigating amplification biases introduced by target­-specific qPCR. Furthermore, the ability to multiplex targets in each well eliminates the need to split valuable samples into multiple reactions. Results from the Circulating microRNA assay are interpreted using Firefly Analysis Workbench, which allows visualization, normalization, and export of experimental data. To aid discovery and validation of biomarkers, we have generated fixed panels for Oncology, Cardiology, Neurology, Immunology, and Liver Toxicology. Here we present the data from several studies investigating circulating and tumor microRNA, showcasing the ability of the technology to sensitively and specifically detect microRNA biomarker signatures from fluid specimens.

Keywords: biomarkers, biofluids, miRNA, photolithography, flowcytometry

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Authors: Abouzar Kaboudian, Boo Cheong Khoo

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The Ghost Solid Method (GSM) based algorithms have been extensively used for numerical calculation of wave propagation in the limit of abrupt changes in materials. In this work, we present a unified version of the GSMs that can be successfully applied to both abrupt as well as smooth changes of the material properties in a medium. The application of this method enables us to use the previously-matured numerical algorithms which were developed to be applied to homogeneous mediums, with only minor modifications. This method is developed for one-dimensional settings and its extension to multi-dimensions is briefly discussed. Various numerical experiments are presented to show the applicability of this unified GSM to wave propagation problems in sharply as well as smoothly varying mediums.

Keywords: elastic solid, functionally graded material, ghost solid method, solid-solid interaction

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Masood Roohi, Amir Taghavipour

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This paper describes a strategy to develop an energy management system (EMS) for a charge-sustaining power-split hybrid electric vehicle. This kind of hybrid electric vehicles (HEVs) benefit from the advantages of both parallel and series architecture. However, it gets relatively more complicated to manage power flow between the battery and the engine optimally. The applied strategy in this paper is based on nonlinear model predictive control approach. First of all, an appropriate control-oriented model which was accurate enough and simple was derived. Towards utilization of this controller in real-time, the problem was solved off-line for a vast area of reference signals and initial conditions and stored the computed manipulated variables inside look-up tables. Look-up tables take a little amount of memory. Also, the computational load dramatically decreased, because to find required manipulated variables the controller just needed a simple interpolation between tables.

Keywords: hybrid electric vehicles, energy management system, nonlinear model predictive control, real-time

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: Kunya Bowornchockchai

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The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins method, Holt’s method, mean absolute percentage error (MAPE), exchange rate

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Authors: David Lindström

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We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

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Authors: R. A. Eman Elsheikh, Bart Schultz, Abraham Mehari Haile, Hussein S. Adam

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A field experiment was conducted at Gezira research station farm during the winter season in the third week of November 2012, in WadMedani, Sudan (Lat 14.23 W, Long 33.39 E and altitude 405 m above sea level, in deep cracking alkaline heavy clay Vertisols). The objective of this study was to determine the effect of three different irrigation for 10 days (W1), 15 days (W2) and 20 days (W3) and for two rows of 30 cm (S1) and 40 cm (S2), respectively. The experimental design was split plot with three replicates. The sunflower test variety was Hysun 33 cultivar. The seasonal water applied during the study was 6898, 6647, 5256, 5435, 5214, 5416 m3/ha for W1S1, W1S2, W2S1, W2S2, W3S1 and W3S2 respectively. The seed yield obtained for the above treatment in that sequence was 4208, 5542, 5167, 4579, 2931, 2936 kg/ha. The corresponding computed water productivity was 0.61, 0.82, 0.87, 0.95, 0.54, 0.56 kg/m3. The study clearly indicated that the highest seed yield was obtained when the crop was sown at 40 cm row spacing and was irrigated every 10 days (W1S2), followed by W2S1.

Keywords: water productivity, water deficit, sunflower, plant spacing

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Authors: Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The discontinuities is characterized using a hybrid spectral/numerical technique. This structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore, the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method proposed.

Keywords: segmentation, s parameters, simulation, optimization

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Authors: Ashish Ankus Yerunkar, Ravi Terkar

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Study aimed at evaluating the best process environment which could simultaneously satisfy requirements of both quality as well as productivity with special emphasis on reduction of cutting tool flank wear, because reduction in flank wear ensures increase in tool life. The predicted optimal setting ensured minimization of surface roughness. Purpose of this paper is focused on the analysis of optimum cutting conditions to get lowest surface roughness in turning SCM 440 alloy steel by Taguchi method. Design for the experiment was done using Taguchi method and 18 experiments were designed by this process and experiments conducted. The results are analyzed using ANOVA method. Taguchi method has depicted that the depth of cut has significant role to play in producing lower surface roughness followed by feed. The Cutting speed has lesser role on surface roughness from the tests. The vibrations of the machine tool, tool chattering are the other factors which may contribute poor surface roughness to the results and such factors ignored for analyses. The inferences by this method will be useful to other researches for similar type of study and may be vital for further research on tool vibrations, cutting forces etc.

Keywords: surface roughness (ra), machining, dry turning, taguchi method, turning process, anova method, mahr perthometer

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Authors: Abdulrahman K. Alshegaifi, Chun-Hsi Huang

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Treating data based on its location in memory has received much attention in recent years due to its different properties, which offer important aspects for cache utilization. Stack data and non-stack data may interfere with each other’s locality in the data cache. One of the important aspects of stack data is that it has high spatial and temporal locality. In this work, we simulate non-unified cache design that split data cache into stack and non-stack caches in order to maintain stack data and non-stack data separate in different caches. We observe that the overall hit rate of non-unified cache design is sensitive to the size of non-stack cache. Then, we investigate the appropriate size and associativity for stack cache to achieve high hit ratio especially when over 99% of accesses are directed to stack cache. The result shows that on average more than 99% of stack cache accuracy is achieved by using 2KB of capacity and 1-way associativity. Further, we analyze the improvement in hit rate when adding small, fixed, size of stack cache at level1 to unified cache architecture. The result shows that the overall hit rate of unified cache design with adding 1KB of stack cache is improved by approximately, on average, 3.9% for Rijndael benchmark. The stack cache is simulated by using SimpleScalar toolset.

Keywords: hit rate, locality of program, stack cache, stack data

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Authors: M. Barański

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The article presents a new vibration diagnostic method designed to (PM) machines with permanent magnets. Those devices are commonly used in small wind and water systems or vehicles drives. The author’s method is very innovative and unique. Specific structural properties of PM machines are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical PM machines and there was no method found to determine the technical condition of such machine basing on their own signals. In this article, the method genesis, the similarity of machines with permanent magnet to vibration sensor and simulation and laboratory tests results will be discussed. The method of determination the technical condition of electrical machine with permanent magnets basing on its own signals is the subject of patent application No P.405669, and it is the main thesis of author’s doctoral dissertation.

Keywords: vibrations, generator, permanent magnet, traction drive, electrical vehicle

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Hong Li, Tingxian Li, Xudong Wang, Weibo Yang

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Co-limitation of iron (Fe) deficiency in legume nitrogen fixation process is not well understood. Our objectives were to examine how peanut plants cope with Fe deficiency with the rhizobial inoculants and N-nutrient treatments. The study was conducted in the tropical Hainan Island during 2012-2013. The soil was strongly acidic (pH 4.6±0.7) and deficient in Fe (9.2±2.3 mg/kg). Peanut plants were intercropped with cassava. The inoculants and N treatments were arranged in a split-plot design with three blocks. Peanut root nodulation, stem allantoin, amino acids and plant N derived from fixation (P) reduced with declining soil Fe concentrations. The treatment interactions were significant on relative ureide % and peanut yields (P<0.05). Residual fixed N from peanut plants was beneficial to cassava plants. It was concluded that co-variance of Fe deficiency could influence peanut N fixation efficiency and rhizobia and N inputs could help improving peanut tolerance to Fe deficiency stress.

Keywords: amino acids, plant N derived from N fixation, root nodulation, soil Fe co-variance, stem ureide, peanuts, cassava

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Authors: M. B. Sokoto, I. U. Abubakar

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The study was carried out on effect of water stress and variety on growth of wheat (Triticum aestivum L.), during 2009/10 and 2010/11 dry seasons. The treatments consisted of factorial combination of water stress at three critical growth stage which was imposed by withholding water at (Tillering, Flowering, Grain filling) and Control (No stress) and two varieties (Star 11 TR 77173/SLM and Kauze/Weaver) laid out in a split-plot design with three replications. Water stress was assigned to the main-plot while variety was assigned to the sub-plots. Result revealed significant (P<0.05) effect of water stress, water stress at tillering significantly (P<0.05) reduced plant height, LAI, CGR, and NAR. Variety had a significant effect on plant height, LAI, CGR and NAR. In conclusion water stress at tillering was observed to be most critical growth stage in wheat, and water stress at this period should be avoided because it results to decrease in growth components in wheat. Wheat should be sown in November or at least first week of December in this area and other area with similar climate. Star II TR 77173/LM is recommended variety for the area.

Keywords: wheat, growth, water stress, variety, Sudan savannah

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Authors: A. Sivakumar, K. Srinivasan

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The main objective of the study is focused in producing slag based geopolymer concrete obtained with the addition of alkali activator. Test results indicated that the reaction of silicates in slag is based on the reaction potential of sodium hydroxide and the formation of alumino-silicates. The study also comprises on the evaluation of the efficiency of polymer reaction in terms of the strength gain properties for different geopolymer mixtures. Geopolymer mixture proportions were designed for different binder to total aggregate ratio (0.3 & 0.45) and fine to coarse aggregate ratio (0.4 & 0.8). Geopolymer concrete specimens casted with normal curing conditions reported a maximum 28 days compressive strength of 54.75 MPa. The addition of glued steel fibres at 1.0% Vf in geopolymer concrete showed reasonable improvements on the compressive strength, split tensile strength and flexural properties of different geopolymer mixtures. Further, comparative assessment was made for different geopolymer mixtures and the reinforcing effects of steel fibres were investigated in different concrete matrix.

Keywords: accelerators, alkali activators, geopolymer, hot air oven curing, polypropylene fibres, slag, steam curing, steel fibres

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Bashara Want

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One of the key factors limiting the performance of magnetic memory is that the coercivity has a distribution with finite width, and the reversal starts at the weakest link in the distribution. So one must first know the distribution of coercivities in order to learn how to reduce the width of distribution and increase the coercivity field to obtain a system with narrow width. First Order Reversal Curve (FORC) method characterizes a system with hysteresis via the distribution of local coercivities and, in addition, the local interaction field. The method is more versatile than usual conventional major hysteresis loops that give only the statistical behaviour of the magnetic system. The FORC method will be presented and discussed at the conference.

Keywords: magnetic materials, hysteresis, first-order reversal curve method, nanostructures

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Authors: A.R. Eskandari, M.R. Eskandari

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A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.

Keywords: inverse scattering, microwave imaging, two-dimensional objects, Linear Sampling Method (LSM)

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Authors: Azizurahman Sakhizadah, Tsugiyuki Masunaga

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The use of sulfur fertilizer by Afghanistan farmers for wheat production has never been practiced, although sulfur deficiency has been expected for wheat production. A field experiment was conducted at Poza e Ishan Research Station Farm, Baghlan province, Afghanistan to examine the effect of sulfur fertilizer on growth and yield components of wheat. The experiment was laid out in randomize complete block design (RCBD), having three replications and eight treatments. The initial soil of experiment was alkaline (pH8.4), with textural class of sandy clay loam, available sulfur (40.8) mg kg-1, and Olsen-P (28.8) mg kg-1. Wheat variety, Kabul 013 was cultivated from November 2015 to June 2016. The recommended doses of nitrogen and Phosphors (Urea and DAP at 250 and 125 kg ha-1) were applied by broadcasting except control plot. Sulfur was applied by foliar spray (K2 SO4) at the rate of 10, 20, and 30 kg ha-1, split at tillering and flowering stages. The results demonstrated that sulfur application positively influenced on growth and yield of wheat crop with combination of nitrogen. Plant did not respond to sole sulfur application. Plant height, spike length, spikelet's number spike-1, were increased and yield g m-2 was also increased by 1.2, 19.1 and 25.1 % for 10, 20 and 30 kg sulfur ha-1 application.

Keywords: sulfur, nitrogen, wheat, foliar

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Authors: Peng Li, Chuanri Li, Tao Li

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Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method and gives concrete processes on determining the factor set, the factor weight set, judgment set, and multi-grade fuzzy comprehensive evaluation. To determine the weight of factor set, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in the fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: reliability allocation, fuzzy arithmetic, allocation weight, linear programming

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: Grzegorz Sierpiński, Ireneusz Celiński, Marcin Staniek

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The article discusses multi modal mobility in contemporary societies as a main planning and organization issue in the functioning of administrative bodies, a problem which really exists in the space of contemporary cities in terms of shaping modern transport systems. The article presents classification of available resources and initiatives undertaken for developing multi modal mobility. Solutions can be divided into three groups of measures–physical measures in the form of changes of the transport network infrastructure, organizational ones (including transport policy) and information measures. The latter ones include in particular direct support for people travelling in the transport network by providing information about ways of using available means of transport. A special measure contributing to this end is a trip planner. The article compares several selected planners. It includes a short description of the Green Travelling Project, which aims at developing a planner supporting environmentally friendly solutions in terms of transport network operation. The article summarizes preliminary findings of the project.

Keywords: mobility, modal split, multimodal trip, multimodal platforms, sustainable transport

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Authors: Aymen Laadhari, Gábor Székely

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This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: finite element method, implicit, level set, membrane, Newton method

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Authors: Angel Pérez Sánchez

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Background: Consider magnetic lines of force as a vector magnetic current was introduced by convention around 1830. But this leads to a dead end in traditional physics, and quantum explanations must be referred to explain the magnetic phenomenon. However, a study of magnetic lines as percussive waves leads to other paths capable of interpreting magnetism through traditional physics. Methodology: Brick used in the experiment: two parallel electric current cables attract each other if current goes in the same direction and its application at a microscopic level inside magnets. Significance: Consideration of magnetic lines as magnets themselves would mean a paradigm shift in the study of magnetism and open the way to provide solutions to mysteries of magnetism until now only revealed by quantum mechanics. Major findings: discover how a magnetic field is created, as well as reason how magnetic attraction and repulsion work, understand how magnets behave when splitting them, and reveal the impossibility of a Magnetic Monopole. All of this is presented as if it were a symphony in which all the notes fit together perfectly to create a beautiful, smart, and simple work.

Keywords: magnetic lines of force, magnetic field, magnetic attraction and repulsion, magnet split, magnetic monopole, magnetic lines of force as magnets, magnetic lines of force as waves

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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Authors: Ayub Khan, Net Ram Garg, Geeta Jain

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In this paper, backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

Keywords: backstepping method, fractional order, synchronization, chaotic system

Procedia PDF Downloads 457