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Co-existence of chaos and stable periodic orbits in a simple discrete neural network. (English) Zbl 1098.37069
Summary: We show that a simple discrete network of two identical neurons can demonstrate chaotic behavior near the origin. This is complementary to the results due to J. Wu and R. Zhang [Discrete Contin. Dyn. Syst., Ser. B 4, 851-863 (2004; Zbl 1115.92003)], where it was shown that the same system can have a large capacity of stable periodic orbits in a region away from the origin.

MSC:
37N25 Dynamical systems in biology
37C27 Periodic orbits of vector fields and flows
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
39A11 Stability of difference equations (MSC2000)
82C32 Neural nets applied to problems in time-dependent statistical mechanics
92B20 Neural networks for/in biological studies, artificial life and related topics
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