Chaos in a Hebbian-type learning algorithm

In this paper, it is shown that a Hebbian-type unsupervised learning algorithm can exhibit chaotic behavior and strange attractors. The Lyapunov exponent and power spectra are presented to confirm the existence of chaotic motion. A chaos-periodic-chaos transition was also observed in this system.

[1]  M. Swamy,et al.  A constrained anti-Hebbian learning algorithm for total least-squares estimation with applications to adaptive FIR and IIR filtering , 1994 .

[2]  B. Ydstie.  Bifurcations and complex dynamics in adaptive control systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[3]  R. Bitmead,et al.  On the dynamics of an equation arising in adaptive control , 1986, 1986 25th IEEE Conference on Decision and Control.

[4]  F. Salam,et al.  Complicated dynamics of prototype continuous-line adaptive control system , 1988 .

[5]  T. Saito,et al.  Chaos from a hysteresis and switched circuit , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[6]  Xiaofeng Liao,et al.  Chaos in a three-neuron hysteresis Hopfield-type neural network☆ , 2001 .

[7]  Jan Willem Polderman,et al.  Dynamics of adaptive systems: A case study , 1996 .

[8]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

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

[10]  B. S. Bourgeois,et al.  Nonlinear behavior of the adaptive LMS algorithm , 1995 .

[11]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[12]  H.H.C. Iu,et al.  Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator , 2000 .

[13]  Leon O. Chua,et al.  Chaos in digital filters , 1988 .

[14]  F. R. Marotto.  Snap-back repellers imply chaos in Rn , 1978 .

[15]  Enric Fossas,et al.  Study of chaos in the buck converter , 1996 .

[16]  Robert R. Bitmead,et al.  Bifurcation effects in robust adaptive control , 1988 .

[17]  L. Chua,et al.  The double scroll family , 1986 .

[18]  P. Das,et al.  Chaos in an effective four-neuron neural network , 1991 .

[19]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[20]  Javier Aracil,et al.  Chaotic motion in an adaptive control system , 1985 .

[21]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[22]  Luigi Glielmo,et al.  Switchings, bifurcations, and chaos in DC/DC converters , 1998 .