By Jean Dieudonne
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Adachi et al. calculated the eigenvalues of the Jacobian Matrix of the CNN and concluded that by using simple chaos control methods, the controlled CNN cannot be stabilized to a stored pattern, and a new control strategy must be developed for the CNN [36]. For the associative memory dynamics, Nakamura et al. [37], Kushibe et al. [38], He et al. [39]–[45], and Shrimali et al. [46]–[47] have proposed some chaos control methods for chaotic neural networks and investigated the controlled dynamics. In this chapter, we focus on several chaos control methods concerned with associative memory and the relation between the stable output and the initial state in the CNN.
65, pp. 3211–3214, 1990. [25] V. Petrov, V. Gaspar, J. Masere, and K. Showwalter, “Controlling chaos in the Belousov–Zhabotinsky reaction,” Nature, vol. 361, pp. 240–243, 1993. [26] R. W. Rollins, P. Parmanada, and P. Sherard, “Controlling chaos in highly dissipative system–a simple recursive algorithm,” Phys. Rev. E, vol. 47, pp. 780–783, 1993. [27] R. Roy, T. W. Murphy, T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser–experimental stabilization of globally coupled system,” Phys.
N, (1) where f (·, a) is a one-dimensional unimodal map with a control parameter a. xn is the value of the state variable at time n, and k represents an additional parameter for constant feedback. The chaotic dynamics can be converted to stable periodic one by tuning k externally [Gueron (1998)]. In what we propose here, we suppose that the dynamical system (see Eq. (1)) possesses a region in the parameter k, where chaotic behaviors are observed with a great number of intermingled periodic windows.