Threshold control of chaotic neural network

The chaotic neural network constructed with chaotic neurons exhibits rich dynamic behaviour with a nonperiodic associative memory. In the chaotic neural network, however, it is difficult to distinguish the stored patterns in the output patterns because of the chaotic state of the network. In order to apply the nonperiodic associative memory into information search, pattern recognition etc. it is necessary to control chaos in the chaotic neural network. We have studied the chaotic neural network with threshold activated coupling, which provides a controlled network with associative memory dynamics. The network converges to one of its stored patterns or/and reverse patterns which has the smallest Hamming distance from the initial state of the network. The range of the threshold applied to control the neurons in the network depends on the noise level in the initial pattern and decreases with the increase of noise. The chaos control in the chaotic neural network by threshold activated coupling at varying time interval provides controlled output patterns with different temporal periods which depend upon the control parameters.

[1]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[2]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[3]  Ping Zhu,et al.  A Type of Delay Feedback Control of Chaotic Dynamics in a Chaotic Neural Network , 2004 .

[4]  Kazuyuki Aihara,et al.  Chaotic simulated annealing by a neural network model with transient chaos , 1995, Neural Networks.

[5]  Liu,et al.  Associative memory with spatiotemporal chaos control. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[7]  Masahiro Nakagawa,et al.  On the Associative Model with Parameter Controlled Chaos Neurons , 1993 .

[8]  K. Aihara,et al.  Chaos and phase locking in normal squid axons , 1987 .

[9]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[10]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[11]  Kazuyuki Aihara,et al.  A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems , 2005, Neural Networks.

[12]  Kazuyuki Aihara,et al.  Chaos control in a neural network with threshold activated coupling , 2007, 2007 International Joint Conference on Neural Networks.

[13]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[14]  Kazuyuki Aihara,et al.  Response Properties of a Single Chaotic Neuron to Stochastic inputs , 2001, Int. J. Bifurc. Chaos.

[15]  Ping Zhu,et al.  Controlling chaos in a chaotic neural network , 2003, Neural Networks.

[16]  Biswas,et al.  Adaptive dynamics on a chaotic lattice. , 1993, Physical review letters.

[17]  Kazuyuki Aihara,et al.  Associative Dynamics in a Chaotic Neural Network , 1997, Neural Networks.

[18]  J. Nagumo,et al.  On a response characteristic of a mathematical neuron model , 1972, Kybernetik.

[19]  Noboru Sonehara,et al.  Controlling Chaos in Chaotic Neural Networks , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[20]  Ping Zhu,et al.  CONTROLLING CHAOS IN A NEURAL NETWORK BASED ON THE PHASE SPACE CONSTRAINT , 2003 .

[21]  T. Kohonen Self-organized formation of topographically correct feature maps , 1982 .

[22]  M. K. Ali,et al.  PATTERN RECOGNITION IN A NEURAL NETWORK WITH CHAOS , 1998 .

[23]  L. Olsen,et al.  Chaos in biological systems. , 1985 .

[24]  Sinha Unidirectional adaptive dynamics. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.