Search results for: 3D-Binary Matrix Reconstruction

Authors: F. Ghaiti

Abstract:

In this paper, we present the 2006 survey study origin destination and price that we carried out during 2006 fall in the area in the Moroccan region of Rabat-Salé-Zemmour-Zaer. The survey concerns the people-s characteristics, their displacements behavior and the price that they will be able to pay for a tramway ticket. The main objective is to study a set of relative features to the households and to their displacement's habits and to their choices among public and privet transport modes. A comparison between this survey results and that of the 1996's is made. A pricing scheme is also given according to the tram capacity. (The Rabat-Salé tramway is under construction right now and it will be operational beginning 2010).

Keywords: Matrix O/D, Theory of pricing, Urban transport survey.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2641

Authors: B. Dahiya, K.Batra, V.Prasad

Abstract:

Artificial atoms are growing fields of interest due to their physical and optoelectronicapplications. The absorption spectra of the proposed artificial atom inpresence of Tera-Hertz field is investigated theoretically. We use the non-perturbativeFloquet theory and finite difference method to study the electronic structure of ArtificialAtom. The effect of static electric field on the energy levels of artificial atom is studied.The effect of orientation of static electric field on energy levels and diploe matrix elementsis also highlighted.

Keywords: Absorption spectra, Artificial atom, Floquet Theory, THz fields

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1699

Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1686

Authors: Yong-jun Zhao, Heng-li Zhang, Zong-yun Hu

Abstract:

Based on the sources- smoothed rank profile (SRP) and modified minimum description length (MMDL) principle, a method for estimation of the source coherency structure (SCS) and the number of wideband sources is proposed in this paper. Instead of focusing, we first use a spatial smoothing technique to pre-process the array covariance matrix of each frequency for de-correlating the sources and then use smoothed rank profile to determine the SCS and the number of wideband sources. We demonstrate the availability of the method by numerical simulations.

Keywords: Wideband sources, source coherency structure (SCS), smoothed rank profile (SRP).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1317

Authors: Hao Wang, Yanming Zou

Abstract:

Two-dimensional (2D) bar codes were designed to carry significantly more data with higher information density and robustness than its 1D counterpart. Thanks to the popular combination of cameras and mobile phones, it will naturally bring great commercial value to use the camera phone for 2D bar code reading. This paper addresses the problem of specific 2D bar code design for mobile phones and introduces a low-level encoding method of matrix codes. At the same time, we propose an efficient scheme for 2D bar codes decoding, of which the effort is put on solutions of the difficulties introduced by low image quality that is very common in bar code images taken by a phone camera.

Keywords: 2D bar code reading, camera phone, low-level encoding, mixed model

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1847

Authors: Chimaobi V. Okolo, Afamefuna J. Ani, Ebere U. Okolo

Abstract:

This paper seeks to assess the implications of insurance to foreign direct investment inflow in Nigeria. Multiple linear regression technique and correlation matrix test were employed to measure the extent to which foreign direct investment was influenced. The result showed that insurance premium (IP), asset size of insurance industry (AS), and total investment of the industry (TI) impacted significantly and positively on foreign direct investment inflow in Nigeria. There should be effective risk transfer mechanism and financial intermediation, which gives the investor confidence in the risk management strength of the host country.

Keywords: Foreign direct investment, insurance.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3048

Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1766

Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

Abstract:

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1661

Authors: O. P. Vinocha , J. S. Bhullar , Manish Gupta

Abstract:

We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length 2a b , a > 0, b is odd.

Keywords: Squaring Construction, generator matrix, selfdual codes, cyclic codes, coset codes, repeated root cycliccodes.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1561

Authors: Atman Jbari, Abdellah Adib, Driss Aboutajdine

Abstract:

This paper addresses the problem of blind source separation (BSS). To recover original signals, from linear instantaneous mixtures, we propose a new contrast function based on the use of a double referenced system. Our approach assumes statistical independence sources. The reference vectors will be incrusted in the cumulant to evaluate the independence. The estimation of the separating matrix will be performed in two steps: whitening observations and joint diagonalization of a set of referenced cumulant matrices. Computer simulations are presented to demonstrate the effectiveness of the suggested approach.

Keywords: Blind source separation, Referenced Cumulant, Contrast, Joint Diagonalization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1018

Authors: H. Assaedi, F. U. A. Shaikh, I. M. Low

Abstract:

Geopolymer composites reinforced with flax fabrics and nanoclay are fabricated and studied for physical and mechanical properties using X-Ray Diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR), and Scanning Electron Microscope (SEM). Nanoclay platelets at a weight of 1.0%, 2.0%, and 3.0% were added to geopolymer pastes. Nanoclay at 2.0 wt.% was found to improve density and decrease porosity while improving flexural strength and post-peak toughness. A microstructural analysis indicated that nanoclay behaves as filler and as an activator supporting geopolymeric reaction while producing a higher content geopolymer gel improving the microstructure of binders. The process enhances adhesion between the geopolymer matrix and flax fibres.

Keywords: Flax fibres, geopolymer, mechanical properties, nanoclay.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1839

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1477

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1618

Authors: Gang Li, Ghulam Mubashar Hassan, Arcady Dyskin, Cara MacNish

Abstract:

Digital image correlation (DIC) is a contactless fullfield displacement and strain reconstruction technique commonly used in the field of experimental mechanics. Comparing with physical measuring devices, such as strain gauges, which only provide very restricted coverage and are expensive to deploy widely, the DIC technique provides the result with full-field coverage and relative high accuracy using an inexpensive and simple experimental setup. It is very important to study the natural patterns effect on the DIC technique because the preparation of the artificial patterns is time consuming and hectic process. The objective of this research is to study the effect of using images having natural pattern on the performance of DIC. A systematical simulation method is used to build simulated deformed images used in DIC. A parameter (subset size) used in DIC can have an effect on the processing and accuracy of DIC and even cause DIC to failure. Regarding to the picture parameters (correlation coefficient), the higher similarity of two subset can lead the DIC process to fail and make the result more inaccurate. The pictures with good and bad quality for DIC methods have been presented and more importantly, it is a systematic way to evaluate the quality of the picture with natural patterns before they install the measurement devices.

Keywords: Digital image correlation (DIC), Deformation simulation, Natural pattern, Subset size.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2799

Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: Graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1233

Authors: Tayeb Lardjane, Rabah Messaci

Abstract:

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1486

Authors: Samra Isadounene, Amar Boukerrou, Dalila Hammiche

Abstract:

In this work, the composites were prepared with poly(lactic acid) (PLA) and olive husk flour (OHF) with different percentages (10, 20 and 30%) using extrusion method followed by injection molding. The morphological, mechanical properties and thermal behavior of composites were investigated. Tensile strength and elongation at break of composites showed a decreasing trend with increasing fiber content. On the other hand, Young modulus and storage modulus were increased. The addition of OHF resulted in a decrease in thermal stability of composites. The presence of OHF led to an increase in percentage of crystallinity (Xc) of PLA matrix.

Keywords: Biopolymers, composites, mechanical properties, poly(lactic acid).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1005

Authors: Paola Gattinoni, Laura Scesi, Elena Cerino Adbin, Daniele Cremonesi

Abstract:

The interaction of tunneling or mining with groundwater has become a very relevant problem not only due to the need to guarantee the safety of workers and to assure the efficiency of the tunnel drainage systems, but also to safeguard water resources from impoverishment and pollution risk. Therefore it is very important to forecast the drainage processes (i.e., the evaluation of drained discharge and drawdown caused by the excavation). The aim of this study was to know better the system and to quantify the flow drained from the Fontane mines, located in Val Germanasca (Turin, Italy). This allowed to understand the hydrogeological local changes in time. The work has therefore been structured as follows: the reconstruction of the conceptual model with the geological, hydrogeological and geological-structural study; the calculation of the tunnel inflows (through the use of structural methods) and the comparison with the measured flow rates; the water balance at the basin scale. In this way it was possible to understand what are the relationships between rainfall, groundwater level variations and the effect of the presence of tunnels as a means of draining water. Subsequently, it the effects produced by the excavation of the mining tunnels was quantified, through numerical modeling. In particular, the modeling made it possible to observe the drawdown variation as a function of number, excavation depth and different mines linings.

Keywords: Groundwater, Italy, numerical model, tunneling.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1928

Authors: P.-W. Tsai, J.-W. Chen, C.-W. Chen, C.-Y. Chen

Abstract:

In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: Half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1920

Authors: I. Ioannou, I. M. Gitman

Abstract:

This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Effective properties, representative volume element, short fiber reinforced composites.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1387

Authors: Udaya Kumar Reddy K. R, K. Viswanathan Iyer

Abstract:

Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n2 log n). This bound is an improvement over previous best known O(n2.376) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matrix multiplication. Our algorithm with slight modifications, enables us to compute the APSP problem for unweighted directed graph in time O(n2 log n), improving a previous best known O(n2.575) time bound of Uri Zwick (2002).

Keywords: Distance in graphs, Dynamic programming, Graphalgorithms, Shortest paths.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3690

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5140

Authors: Kavita Khairnar, Shikha Nema

Abstract:

DS-CDMA system is well known wireless technology. This system suffers from MAI (Multiple Access Interference) caused by Direct Sequence users. Multi-User Detection schemes were introduced to detect the users- data in presence of MAI. This paper focuses on linear multi-user detection schemes used for data demodulation. Simulation results depict the performance of three detectors viz-conventional detector, Decorrelating detector and Subspace MMSE (Minimum Mean Square Error) detector. It is seen that the performance of these detectors depends on the number of paths and the length of Gold code used.

Keywords: Cross Correlation Matrix, MAI, Multi-UserDetection, Multipath Effect.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2113

Authors: Uma Thanganathan

Abstract:

The hybrid membranes containing inorganic materials in polymer matrix are identified as a remarkable family of proton conducting hybrid electrolytes. In this work, the proton conducting inorganic/organic hybrid membranes for proton exchange membrane fuel cells (PEMFCs) were prepared using polyvinyl alcohol (PVA), tetraethoxyorthosilane (TEOS) and heteropolyacid (HPA). The synthesized hybrid membranes were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction spectroscopy (XRD), Scanning electron microscopy (SEM) and Thermogravimetry analysis (TGA). The effects of heteropolyacid incorporation on membrane properties, including morphology and thermal stability were extensively investigated.

Keywords: PEMFC, Hybrid membrane, FTIR, TGA, Phosphomolybdic acid

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2597

Authors: Priyankar Pratim Deka, Sutanu Samanta

Abstract:

This paper describes the development of new class of epoxy based rice husk filled jute reinforced composites. Rice husk flour is added in 0%, 1%, 3%, 5% by weight. Epoxy resin and triethylenetetramine (T.E.T.A) is used as matrix and hardener respectively. It investigates the mechanical properties of the composites and a comparison is done for monolithic jute composite and the filled ones. The specimens are prepared according to the ASTM standards and experimentation is carried out using INSTRON 8801. The result shows that with the increase of filler percentage the tensile properties increases but compressive and flexural properties decreases.

Keywords: Jute, mechanical characterization, natural fiber, rice husk.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2063

Authors: Abdelmalek Fermas, Adel Belouchrani, Otmane Ait Mohamed

Abstract:

In Blind Source Separation (BSS) processing, taking advantage of scaling factor indetermination and based on the floatingpoint representation, we propose a scaling technique applied to the separation matrix, to avoid the saturation or the weakness in the recovered source signals. This technique performs an Automatic Gain Control (AGC) in an on-line BSS environment. We demonstrate the effectiveness of this technique by using the implementation of a division free BSS algorithm with two input, two output. This technique is computationally cheaper and efficient for a hardware implementation.

Keywords: Automatic Gain Control, Blind Source Separation, Floating-Point Representation, FPGA Implementation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1520

Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1819

Authors: A. Thabet, G. B. H. Frej, M. Boutayeb

Abstract:

This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot.

Keywords: Feedback stabilization, DMVT, Lipschitz nonlinear systems, nonlinear observer, real time implementation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1361

Authors: A. Shaygani, R. Saifi, M. S. Saidi, M. Sani

Abstract:

Particle size distribution, the most important characteristics of aerosols, is obtained through electrical characterization techniques. The dynamics of charged nanoparticles under the influence of electric field in Electrical Mobility Spectrometer (EMS) reveals the size distribution of these particles. The accuracy of this measurement is influenced by flow conditions, geometry, electric field and particle charging process, therefore by the transfer function (transfer matrix) of the instrument. In this work, a wire-cylinder corona charger was designed and the combined fielddiffusion charging process of injected poly-disperse aerosol particles was numerically simulated as a prerequisite for the study of a multichannel EMS. The result, a cloud of particles with no uniform charge distribution, was introduced to the EMS. The flow pattern and electric field in the EMS were simulated using Computational Fluid Dynamics (CFD) to obtain particle trajectories in the device and therefore to calculate the reported signal by each electrometer. According to the output signals (resulted from bombardment of particles and transferring their charges as currents), we proposed a modification to the size of detecting rings (which are connected to electrometers) in order to evaluate particle size distributions more accurately. Based on the capability of the system to transfer information contents about size distribution of the injected particles, we proposed a benchmark for the assessment of optimality of the design. This method applies the concept of Von Neumann entropy and borrows the definition of entropy from information theory (Shannon entropy) to measure optimality. Entropy, according to the Shannon entropy, is the ''average amount of information contained in an event, sample or character extracted from a data stream''. Evaluating the responses (signals) which were obtained via various configurations of detecting rings, the best configuration which gave the best predictions about the size distributions of injected particles, was the modified configuration. It was also the one that had the maximum amount of entropy. A reasonable consistency was also observed between the accuracy of the predictions and the entropy content of each configuration. In this method, entropy is extracted from the transfer matrix of the instrument for each configuration. Ultimately, various clouds of particles were introduced to the simulations and predicted size distributions were compared to the exact size distributions.

Keywords: Aerosol Nano-Particle, CFD, Electrical Mobility Spectrometer, Von Neumann entropy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1859

Authors: Kaihong Zhao

Abstract:

In this paper, the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin-s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Nonautonomous Lotka-Volterra cooperative system, Coincidence degree, Harvesting term.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1336