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Chaos in a three-dimensional general model of neural network. (English) Zbl 1043.37512
Summary: The dynamics of a network of three neurons with all possible connections is studied. The equations of control are given by three differential equations with nonlinear, positive and bounded sigmoidal response function of the neurons. The system passes from stable to periodic and then to chaotic regimes and returns to a stationary regime with change in parameter values of synaptic weights and decay rates. We developed programs and used the Locbif package to study phase portraits, bifurcation diagrams which confirm the result. Lyapunov exponents are calculated to confirm chaos.
MSC:
37N25Dynamical systems in biology
37D45Strange attractors, chaotic dynamics
82C32Neural nets (statistical mechanics)
92B20General theory of neural networks (mathematical biology)