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Zbl 0782.92003
Zou, Fan; Nossek, Josef A.
Bifurcation and chaos in cellular neural networks. (English)
[J] IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 40, No.3, 166-173 (1993). ISSN 1057-7122

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 2000:: *92B20 General theory of neural networks
34C05 Qualitative theory of some special solutions of ODE
37N99 Applications of dynamical systems
37D45 Strange attractors, chaotic dynamics

Keywords: cellular neural networks; two-cell autonomous system; Hopf-like bifurcation; limit cycle; three-cell autonomous system; chaotic attractor; double scroll attractor

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