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【期刊论文】Global continuation of nonlinear waves in a ring of neurons
郭上江, Shangjiang Guo and Lihong Huang
Proceedings of the Royal Society of Edinburgh, 135A, 999-1015, 2005,-0001,():
-1年11月30日
In this paper, we consider a ring of neurons with self-feedback and delays. As a result of our approach based on global bifurcation theorems of delay differential equations coupled with representation theory of Lie groups, the coexistence of its asynchronous periodic solutions (i.e. mirror-reflecting waves, standing waves and discrete waves), bifurcated simultaneously from the trivial solution at some critical values of the delay, will be established for delay not only near to but also far away from the critical values. Therefore, we can obtain wave solutions of large amplitudes. In addition, we consider the coincidence of these periodic solutions.
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【期刊论文】Hopf bifurcating periodic orbits in a ring of neurons with delays
郭上江, Shangjiang Guo*, Lihong Huang
Physica D 183(2003)19-44,-0001,():
-1年11月30日
In this paper, we consider a ring of neurons with self-feedback and delays. The linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, we derive the formula for determining the properties of Hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays, including the direction of Hopf bifurcation, stability of the Hopf bifurcating slowly oscillating periodic orbits, and so on. Moreover, by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups, we not only investigate the effect of synaptic delay of signal transmission on the pattern formation, but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio-temporal patterns.
A ring of neurons, Hopf bifurcation, Slowly oscillating periodic solution, Lie group
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【期刊论文】Regular dynamics in a delayed network of two neurons with all-or-none activation functions
郭上江, Shangjiang Guo a, *, Lihong Huang a, Jianhong Wu b
Physica D 206(2005)32-48,-0001,():
-1年11月30日
We consider a delayed network of two neurons with both self-feedback and interaction described by an all-or-none threshold function. The model describes a combination of analog and digital signal processing in the network and takes the form of a system of delay differential equations with discontinuous nonlinearity.We show that the dynamics of the network can be understood in terms of the iteration of a one-dimensional map, and we obtain simple criteria for the convergence of solutions, the existence, multiplicity and attractivity of periodic solutions. © 2005 Elsevier B.V. All rights reserved.
Neural networks, Delayed feedback, One-dimensional map, Convergence, Periodic solutions
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【期刊论文】Global existence of periodic solutions of BAM neural networks with variable coefficients ☆
郭上江, Shangjiang Guo a, *, Lihong Huang a, Binxiang Dai a, Zhongzhi Zhang b
Physics Letters A 317(2003)97-106,-0001,():
-1年11月30日
In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays. © 2003 Elsevier B.V. All rights reserved.
Periodic solution, BAM neural networks, Coincidence degree
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【期刊论文】Stability analysis of a delayed Hopfield neural network
郭上江, Shangjiang Guo* and Lihong Huang
PHYSICAL REVIEW E 67, 061902(2003),-0001,():
-1年11月30日
In this paper, we study a class of neural networks, which includes bidirectional associative memory networks and cellular neural networks as its special cases. By Brouwer's fixed point theorem, a continuation theorem based on Gains and Mawhin's coincidence degree, matrix theory, and inequality analysis, we not only obtain some different sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity.
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