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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:
37N25Dynamical systems in biology
37C27Periodic orbits of vector fields and flows
37D45Strange attractors, chaotic dynamics
39A11Stability of difference equations (MSC2000)
82C32Neural nets (statistical mechanics)
92B20General theory of neural networks (mathematical biology)