Search results for: Linear fredholm equations

Authors: H. Sadjadian , H.D. Taghirad Member, A. Fatehi

Abstract:

In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

Keywords: Forward Kinematics, Neural Networks, Numerical Solution, Parallel Manipulators.

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

Authors: Kirill Trapezon, Alexandr Trapezon

Abstract:

A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: Vibrations, plate, thickness, symmetry, factorization, approximation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 796

Authors: Ali Mchirgui, Nejib Hidouri, Mourad Magherbi, Ammar Ben Brahim

Abstract:

The paper provides a numerical investigation of the entropy generation analysis due to natural convection in an inclined square porous cavity. The coupled equations of mass, momentum, energy and species conservation are solved using the Control Volume Finite-Element Method. Effect of medium permeability and inclination angle on entropy generation is analysed. It was found that according to the Darcy number and the porous thermal Raleigh number values, the entropy generation could be mainly due to heat transfer or to fluid friction irreversibility and that entropy generation reaches extremum values for specific inclination angles.

Keywords: Porous media, entropy generation, convection, numerical method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2607

Authors: Cheika Jahangeer, Naushad Mamode Khan, Maleika Heenaye-Mamode Khan

Abstract:

Exclusive breastfeeding is the feeding of a baby on no other milk apart from breast milk. Exclusive breastfeeding during the first 6 months of life is of fundamental importance because it supports optimal growth and development during infancy and reduces the risk of obliterating diseases and problems. Moreover, in developed countries, exclusive breastfeeding has decreased the incidence and/or severity of diarrhea, lower respiratory infection and urinary tract infection. In this paper, we study the factors that influence exclusive breastfeeding and use the Generalized Poisson regression model to analyze the practices of exclusive breastfeeding in Mauritius. We develop two sets of quasi-likelihood equations (QLE)to estimate the parameters.

Keywords: Exclusive breastfeeding, Regression model, Quasilikelihood.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1801

Authors: I. Naeem, R. Naz

Abstract:

The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.

Keywords: Two-dimensional jets, radial jets, group invariant solution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1457

Authors: Abdulaziz Alsadhan, Naveed Khan

Abstract:

In recent years intrusions on computer network are the major security threat. Hence, it is important to impede such intrusions. The hindrance of such intrusions entirely relies on its detection, which is primary concern of any security tool like Intrusion detection system (IDS). Therefore, it is imperative to accurately detect network attack. Numerous intrusion detection techniques are available but the main issue is their performance. The performance of IDS can be improved by increasing the accurate detection rate and reducing false positive. The existing intrusion detection techniques have the limitation of usage of raw dataset for classification. The classifier may get jumble due to redundancy, which results incorrect classification. To minimize this problem, Principle component analysis (PCA), Linear Discriminant Analysis (LDA) and Local Binary Pattern (LBP) can be applied to transform raw features into principle features space and select the features based on their sensitivity. Eigen values can be used to determine the sensitivity. To further classify, the selected features greedy search, back elimination, and Particle Swarm Optimization (PSO) can be used to obtain a subset of features with optimal sensitivity and highest discriminatory power. This optimal feature subset is used to perform classification. For classification purpose, Support Vector Machine (SVM) and Multilayer Perceptron (MLP) are used due to its proven ability in classification. The Knowledge Discovery and Data mining (KDD’99) cup dataset was considered as a benchmark for evaluating security detection mechanisms. The proposed approach can provide an optimal intrusion detection mechanism that outperforms the existing approaches and has the capability to minimize the number of features and maximize the detection rates.

Keywords: Particle Swarm Optimization (PSO), Principle component analysis (PCA), Linear Discriminant Analysis (LDA), Local Binary Pattern (LBP), Support Vector Machine (SVM), Multilayer Perceptron (MLP).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2765

Authors: Hosein Shokohmand, Mahmood Hosein Zare, Abdorreza Qolibeik

Abstract:

In this paper, the effects of thermodynamic, hydrodynamic and geometric of an air cooled condenser on COP of vapor compression cycle are investigated for a fixed condenser facing surface area. The system is utilized with a scroll compressor, modeled based on thermodynamic and heat transfer equations employing Matlab software. The working refrigerant is R134a whose thermodynamic properties are called from Engineering Equation Software. This simulation shows that vapor compression cycle can be designed by different configurations and COPs, economical and optimum working condition can be obtained via considering these parameters.

Keywords: Vapor compression cycle, air cooled condenser, COP, heat exchanger, thermal modeling.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1964

Authors: Debasis Sarkar, Jatan Talati

Abstract:

This paper is an attempt to develop an Integrated Mass Rapid Transit System (MRTS) for a smart city project in Western India. Integrated transportation is one of the enablers of smart transportation for providing a seamless intercity as well as regional level transportation experience. The success of a smart city project at the city level for transportation is providing proper integration to different mass rapid transit modes by way of integrating information, physical, network of routes fares, etc. The methodology adopted for this study was primary data research through questionnaire survey. The respondents of the questionnaire survey have responded on the issues about their perceptions on the ways and means to improve public transport services in urban cities. The respondents were also required to identify the factors and attributes which might motivate more people to shift towards the public mode. Also, the respondents were questioned about the factors which they feel might restrain the integration of various modes of MRTS. Furthermore, this study also focuses on developing a utility equation for respondents with the help of multiple linear regression analysis and its probability to shift to public transport for certain factors listed in the questionnaire. It has been observed that for shifting to public transport, the most important factors that need to be considered were travel time saving and comfort rating. Also, an Integrated MRTS can be obtained by combining metro rail with BRTS, metro rail with monorail, monorail with BRTS and metro rail with Indian railways. Providing a common smart card to transport users for accessing all the different available modes would be a pragmatic solution towards integration of the available modes of MRTS.

Keywords: Mass rapid transit systems, smart city, metro rail, bus rapid transit system, multiple linear regression, smart card, automated fare collection system.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1226

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1485

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

Abstract:

In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1161

Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1588

Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1680

Authors: Gilberto Gonzalez-A, Ignacio Rodríguez- A., Dunia Nuñez-P

Abstract:

A bond graph model of a two degrees of freedom PUMA is described. System inversion gives the system input required to generate a given system output. In order to get the system inversion of the PUMA manipulator, a linearization of the nonlinear bond graph is obtained. Hence, the bicausality of the linearized bond graph of the PUMA manipulator is applied. Thus, the bicausal bond graph provides a systematic way of generating the equations of the system inversion. Simulation results to verify the calculated input for a given output are shown.

Keywords: Bond graph, system inversion, bicausality, PUMA manipulator

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2012

Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2002

Authors: Y.Bakhshan, H.Ashoori

Abstract:

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Keywords: Rectangular Cavity, magneto-hydrodynamic, free convection, simulation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1583

Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

Abstract:

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: Thermoelasticity, three-dimensional, Laplace transforms, Fourier transforms, thermal conductivity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 749

Authors: Shih-Ching Lo

Abstract:

Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1463

Authors: T. Messikh, S. Mekhilef, N. A. Rahim

Abstract:

This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.

Keywords: Adaptive notch filter, Active power filter, harmonic filtering, Time varying frequency.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3053

Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3076

Authors: Abdullah Al Faruque, Ram Balachandar

Abstract:

Series of laboratory tests were carried out to study the extent of scour caused by a three-dimensional wall jets exiting from a square cross-section nozzle and into a non-cohesive sand beds. Previous observations have indicated that the effect of the tail water depth was significant for densimetric Froude number greater than ten. However, the present results indicate that the cut off value could be lower depending on the value of grain size-to-nozzle width ratio. Numbers of equations are drawn out for a better scaling of numerous scour parameters. Also suggested the empirical prediction of scour to predict the scour centre line profile and plan view of scour profile at any particular time.

Keywords: Densimetric Froude Number, Jets, Nozzle, Sand, Scour, Tailwater, Time.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1980

Authors: Changzhao Li, Juan Zhang

Abstract:

In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.

Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1344

Authors: Alok Madan, Arshad K. Hashmi

Abstract:

The paper presents a plastic analysis procedure based on the energy balance concept for performance based seismic retrofit of multi-story multi-bay masonry infilled reinforced concrete (R/C) frames with a ‘soft’ ground story using passive energy dissipation (PED) devices with the objective of achieving a target performance level of the retrofitted R/C frame for a given seismic hazard level at the building site. The proposed energy based plastic analysis procedure was employed for developing performance based design (PBD) formulations for PED devices for a simulated application in seismic retrofit of existing frame structures designed in compliance with the prevalent standard codes of practice. The PBD formulations developed for PED devices were implemented for simulated seismic retrofit of a representative code-compliant masonry infilled R/C frame with a ‘soft’ ground story using friction dampers as the PED device. Non-linear dynamic analyses of the retrofitted masonry infilled R/C frames is performed to investigate the efficacy and accuracy of the proposed energy based plastic analysis procedure in achieving the target performance level under design level earthquakes. Results of non-linear dynamic analyses demonstrate that the maximum inter-story drifts in the masonry infilled R/C frames with a ‘soft’ ground story that is retrofitted with the friction dampers designed using the proposed PBD formulations are controlled within the target drifts under near-field as well far-field earthquakes.

Keywords: Energy Methods, Masonry Infilled Frame, Near-field Earthquakes, Seismic Protection, Supplemental damping devices.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2542

Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1720

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

Abstract:

Sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: Sampled-data control, Sector bound, Solid oxide fuel cell, Time-delay.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1723

Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3002

Authors: Farhad Kolahan, Mohammad Bironro

Abstract:

This paper addresses modeling and optimization of process parameters in powder mixed electrical discharge machining (PMEDM). The process output characteristics include metal removal rate (MRR) and electrode wear rate (EWR). Grain size of Aluminum powder (S), concentration of the powder (C), discharge current (I) pulse on time (T) are chosen as control variables to study the process performance. The experimental results are used to develop the regression models based on second order polynomial equations for the different process characteristics. Then, a genetic algorithm (GA) has been employed to determine optimal process parameters for any desired output values of machining characteristics.

Keywords: Regression modeling, PMEDM, GeneticAlgorithm, Optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1493

Authors: Jaroslav Žák, Aleš Florian

Abstract:

Green bridges enable wildlife to pass through linear structures, especially freeways. The term migration potential is used to quantify their functionality. The proposed methodology for determining migration potential eliminates the mathematical, systematic and ecological inaccuracies of previous methodologies and provides a reliable tool for designers and environmentalists. The methodology is suited especially to medium-sized and large mammals, is mathematically correct, and its correspondence with reality was tested by monitoring existing green bridges. 

Keywords: Green bridges, migration potential, partial probabilities, wildlife migration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1754

Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2214

Authors: A. Johannet, B. Vayssade, D. Bertin

Abstract:

Neural networks are well known for their ability to model non linear functions, but as statistical methods usually does, they use a no parametric approach thus, a priori knowledge is not obvious to be taken into account no more than the a posteriori knowledge. In order to deal with these problematics, an original way to encode the knowledge inside the architecture is proposed. This method is applied to the problem of the evapotranspiration inside karstic aquifer which is a problem of huge utility in order to deal with water resource.

Keywords: Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1808

Authors: Changjin Xu

Abstract:

In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.

Keywords: Two-neuron system, delay, stability, Hopf bifurcation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1326