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Dynamics of a two-neuron system with discrete and distributed delays
2004
Physica D : Non-linear phenomena
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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
2019
IEEE Access
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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
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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
2021
Complexity
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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
2014
Advances in Artificial Neural Systems
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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
2008
Nonlinear Analysis: Modelling and Control
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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]
2009
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
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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
2007
The European Physical Journal Special Topics
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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
1994
Neural Computation
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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
2014
Abstract and Applied Analysis
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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
2009
Nonlinear Analysis: Modelling and Control
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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]
2013
Artificial Neural Networks - Architectures and Applications
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:1909.08341v2 fatcat:5oyropzd3zawdeyzfabphwjr7qOther Versions
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
1996
SIAM Journal on Applied Mathematics
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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
2022
Mathematical Problems in Engineering
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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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