Markov Chain Modeling of Intermittency Chaos and Its Application to Hopfield NN

SUMMARY In this study, a modeling method of the intermittency chaos using the Markov chain is proposed. The performances of the intermittency chaos and the Markov chain model are investigated when they are injected to the Hopfield Neural Network for a quadratic assignment problem or an associative memory. Computer simulated results show that the proposed modeling is good enough to gain similar performance of the intermittency chaos.

[1]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[2]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[4]  S. E. Karisch,et al.  QAPLIB-A quadratic assignment problem library , 1991 .

[5]  Hayakawa,et al.  Effects of the chaotic noise on the performance of a neural network model for optimization problems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Franz Rendl,et al.  QAPLIB – A Quadratic Assignment Problem Library , 1997, J. Glob. Optim..

[7]  H. Dedieu Overview of nonlinear noise reduction algorithms for systems with known dynamics , 1998 .

[8]  Gianluca Mazzini,et al.  A tensor approach to higher order expectations of quantized chaotic trajectories. I. General theory and specialization to piecewise affine Markov systems , 2000 .

[9]  Gianluca Mazzini,et al.  Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems. II. Higher order correlations and self-similarity , 2002 .

[10]  Yoko Uwate,et al.  Performance of Chaos Noise Injected to Hopfield NN for Quadratic Assignment Problems , 2002 .

[11]  Y. Nishio,et al.  Associative memory by Hopfield NN with chaos injection , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).