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A bifurcation analysis of the four dimensional generalized Hopfield neural network. (English) Zbl 0894.58048

Summary: A four neuron Hopfield neural network with asymmetric weights and self-connection is analyzed. Its stable steady state and periodic attractors are identified and a complete bifurcation diagram is constructed. A center manifold reduction is undertaken and by means of normal form theory, the characteristics of the limit cycles are obtained. The network is seen to have a large memory storage capacity with both fixed point and periodic memories coexisting. The onset of chaos as reported previously is considered.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
68T05 Learning and adaptive systems in artificial intelligence
82C32 Neural nets applied to problems in time-dependent statistical mechanics
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