Co-existence of chaos and stable periodic orbits in a simple discrete neural network. (English) Zbl 1098.37069

Huang, Yu; Zou, X.

J. Nonlinear Sci. 15, No. 5, 291-303 (2005).

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

Keywords:

neural network; discrete; delay; chaos; capacity; associate memory; periodic solutions

Citations:

Zbl 1115.92003