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Dynamics of a two-neuron system with discrete and distributed delays

S Ruan
2004 Physica D : Non-linear phenomena  
In this paper we consider a two-neuron network model with multiple discrete and distributed delays, where the distributed delays describe the neural feedback and the discrete delays describe the neural  ...  Three special cases of the artificial neural network model are considered.  ...  Acknowledgements Research was partially supported by the Natural Science and Engineering Research Council (NSERC) of Canada and a start-up grant from the College of Arts and Sciences at the University  ... 
doi:10.1016/j.physd.2003.12.004 fatcat:eftou4fc75b2vgoyc2gnrrficy

Dynamics of fractional-order neural networks with discrete and distributed delays

Lingzhi Si, Min Xiao, Min Xiao, Guoping Jiang, Zunshui Cheng, Qiankun Song, Jinde Cao
2019 IEEE Access  
This paper is concerned with the stability and Hopf bifurcation of fractional-order neural networks with discrete and distributed delays.  ...  By introducing two virtual neurons to the original network, a new four-neuron network only involving discrete delays is formed.  ...  Henceforth, more and more scholars set out to construct artificial neural network models with time delay so as to get close to biological neural networks.  ... 
doi:10.1109/access.2019.2946790 fatcat:jievokmqrbewjmnq4lldfi473i

Page 7023 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
periodic orbits in a ring of neurons with delays.  ...  In this paper, the author studies the globai asymptotic stability of a system of cellular neural networks with fixed time delays.  ... 

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Li Cui, Chaoyang Chen, Jie Jin, Fei Yu, Chong Fu
2021 Complexity  
Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network (CNN) model.  ...  A neural network is a model of the brain's cognitive process, with a highly interconnected multiprocessor architecture.  ...  McCulloch and Pitts abstracted human brain neurons and built a simple model to form a neural network, namely, artificial neural network [1] .  ... 
doi:10.1155/2021/5521192 fatcat:7iffgrestbgntksw2wduifbeo4

Oscillatory Behavior on a Three-Node Neural Network Model with Discrete and Distributed Delays

Chunhua Feng
2014 Advances in Artificial Neural Systems  
This paper investigates the oscillatory behavior of the solutions for a three-node neural network with discrete and distributed delays.  ...  Two theorems are provided to determine the conditions for oscillating solutions of the model. The criteria for selecting the parameters in this network are derived.  ...  Ruan and Filfil [2] considered a two-neuron network model with multiple discrete and distributed delays as follows: where the delayed feedback kernel satisfies ∫ .  ... 
doi:10.1155/2014/536324 fatcat:sbvbtbvo2vhw7brafqrd47trdy

Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay

P. D. Gupta, N. C. Majee, A. B. Roy
2008 Nonlinear Analysis: Modelling and Control  
A distributed delay model of a class of three-neuron network has been investigated.  ...  A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution occurs for each point of such interval.  ...  Two Neuron systems with distributed delay have been studied in papers [30, 31] . Three neuron network with discrete delays has been studied in [32] [33] [34] [35] .  ... 
doi:10.15388/na.2008.13.1.14586 fatcat:equu3dvnubevva2sx5sbk2oqam

Chaotic and Hyperchaotic Attractors in Time-Delayed Neural Networks [chapter]

Dong Zhang, Jian Xu
2009 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
It is well known that complex dynamic behaviors exist in time-delayed neural networks.  ...  This paper presents an infinite-dimension hyperchaotic time-delayed neuron system with sinusoidal activation function.  ...  Background of the Model A class of artificial neural network with single delay considered in this Letter is described by the following differential equations with delay: ( ) ( ) 1 1 ( ) ( ) ( ) ( ) ,  ... 
doi:10.1007/978-3-642-02469-6_1 fatcat:ffczqwkur5a43dcbmxpd6onz2i

Introduction

B. Cessac, E. Daucé, L. Perrinet, M. Samuelides
2007 The European Physical Journal Special Topics  
Perceptron's controversy between "Symbolic Artificial Intelligence" and "Distributed Neural Computation" delayed considerably applied research in the field of artificial neural networks but still had the  ...  Therefore, the joint modeling and control of these two dynamics in artificial neural networks reveals to be a real challenge.  ... 
doi:10.1140/epjst/e2007-00057-3 fatcat:3xvewhthf5a6rjyo4biso3ig4a

Dimension Reduction of Biological Neuron Models by Artificial Neural Networks

Kenji Doya, Allen I. Selverston
1994 Neural Computation  
We propose an artificial neural network approach to reduction of conductance-based models. Learning in artificial neural networks is a practical method for constructing a model from examples.  ...  A. 1989. Learning state space trajectories in recurrent neural networks. Neural Comp. 1, 263-269. Plant, R. E. 1981. Bifurcation and resonance in a model for bursting neurons. J. Math.  ... 
doi:10.1162/neco.1994.6.4.696 fatcat:gfalfsx2onhxxbqegxdf7nradq

Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling

Jiao Jiang, Yongli Song
2014 Abstract and Applied Analysis  
We investigate the dynamics of a delayed neural network model consisting ofnidentical neurons.  ...  Finally, two neural network models with four or seven neurons are used to verify our theoretical results.  ...  Innovation Program of Shanghai Municipal Education Commission (no. 14YZ114), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, and the Program for New Century Excellent Talents in  ... 
doi:10.1155/2014/368652 fatcat:jdbir6mpjffqhgtorvql24gpce

Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

P. D. Gupta, N. C. Majee, A. B. Roy
2009 Nonlinear Analysis: Modelling and Control  
In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated.  ...  The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay.  ...  Thus delay is an important controlled parameter in neural system. Delays may be discrete or continuous in nature. We have considered here a three neuron BAM network with distributed delay.  ... 
doi:10.15388/na.2009.14.4.14466 fatcat:cfvi4ddtbbdalamugqcnpjqqxi

Biologically Plausible Artificial Neural Networks [chapter]

Joao Luis Garcia Rosa
2013 Artificial Neural Networks - Architectures and Applications  
Classical ANN models Classical artificial neural networks models are based upon a simple description of the neuron, taking into account the presence of presynaptic cells and their synaptic potentials,  ...  They are simple neural structures of limited applications [30]; (2) the second generation deals with complex dynamics with recurrent networks in order to deal with spatio-temporal events; (3) the third  ...  Acknowledgements I am grateful to my students, who have collaborated with me in this subject for the last ten years.  ... 
doi:10.5772/54177 fatcat:xeavo23zinczve6n6ovdkf226q

Bifurcation Spiking Neural Network [article]

Shao-Qun Zhang and Zhao-Yu Zhang and Zhi-Hua Zhou
2021 arXiv   pre-print
Spiking neural networks (SNNs) has attracted much attention due to its great potential of modeling time-dependent signals.  ...  The firing rate of spiking neurons is decided by control rate which is fixed manually in advance, and thus, whether the firing rate is adequate for modeling actual time series relies on fortune.  ...  In general, we can also add a learning rate η to help convergence, just like most deep artificial neural networks. Here, BSNN is implemented by an extended BP algorithm.  ... 
arXiv:1909.08341v3 fatcat:rzahgfwckrfqxajtbrpcrp7cja

Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model

Jacques Bélair, Sue Ann Campbell, P. van den Driessche
1996 SIAM Journal on Applied Mathematics  
The effect of time delays on the linear stability of equilibria in an artificial neural network of Hopfield type is analyzed.  ...  Nonlinear analysis (centre manifold computation) of a three-unit frustrated network is presented, giving the nature of the bifurcations taking place.  ...  As a neural network model, independent of a physical realization, (2.3 holds without the normalisation condition.  ... 
doi:10.1137/s0036139994274526 fatcat:whzxabgrt5d43biyfsb32bt4ei

Economic Forecasting Model Based on Chaos Simulated Annealing Neural Network

Qing Zhang, Yuning Mu, Wen-Tsao Pan
2022 Mathematical Problems in Engineering  
In view of the prototype of the traditional chaotic network model, a neural network model with continuously updated chaotic noise is innovatively improved.  ...  In order to effectively alleviate the predictive control problem of nonlinear research objects, we propose a control method based on chaotic neural network in this study.  ...  Conflicts of Interest e authors declare that they have no conflicts of interest or personal relationships that could have appeared to influence the work reported in this paper.  ... 
doi:10.1155/2022/9005833 fatcat:ac6t32trlja77j2wzzgvrt32ha
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