Europhys. Lett., 62 (5) , pp. 657-663 (2003)
Low-dimensional chaos induced by frustration in a non-monotonic systemM. Kawamura1, R. Tokunaga2 and M. Okada3
1 Faculty of Science, Yamaguchi University Yoshida 1677-1, Yamaguchi, 753-8512 Japan
2 Institute of Information Sciences and Electronics, University of Tsukuba Tennodai 1-1-1, Tsukuba, 305-8573 Japan
3 Brain Science Institute, RIKEN - Wako-shi, 351-0198 Japan
(Received 30 September 2002; accepted in final form 7 April 2003)
We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order parameter equations. Then we analytically show that chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that chaos definitely does not occur without frustration.
05.45.Ac - Low-dimensional chaos.
02.70.Rr - General statistical methods.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
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