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Local activity criteria for discrete-map CNN. (English) Zbl 1051.82518
Summary: Discrete-time CNN systems are studied in this paper by the application of Chua’s local activity principle. These systems are locally active everywhere except for one isolated parameter value. As a result, nonhomogeneous spatiotemporal patterns may be induced by any initial setting of the CNN system when the strength of the system diffusion coupling exceeds a critical threshold. The critical coupling coefficient can be derived from the loaded cell impedance of the CNN system. Three well-known 1D map CNN’s (namely, the logistic map CNN, the magnetic vortex pinning map CNN, and the spiral wave reproducing map CNN) are introduced to illustrate the applications of the local activity principle. In addition, we use the cell impedance to demonstrate the period-doubling scenario in the logistic and the magnetic vortex pinning maps
MSC:
82C32Neural nets (statistical mechanics)
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)