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Bifurcation and chaos in cellular neural networks. (English) Zbl 0782.92003
Summary: Bifurcation phenomena and chaotic behavior in cellular neural networks are investigated. In a two-cell autonomous system, Hopf-like bifurcation has been found, at which the flow around the origin, an equilibrium point of the system, changes from asymptotically stable to periodic. As the parameter grows further, by reaching another bifurcation value, the generated limit cycle disappears and the network becomes convergent again. Chaos is also presented in a three-cell autonomous system. It is shown that the chaotic attractor found here has properties similar to the famous double scroll attractor.
MSC:
92B20General theory of neural networks (mathematical biology)
34C05Location of integral curves, singular points, limit cycles (ODE)
37N99Applications of dynamical systems
37D45Strange attractors, chaotic dynamics