Chaos in a three dimensional neural network
Applied Mathematical ModellingPublished 1 June 2000
Atin Das, Abhinaba Roy, Pritha Das
Citations56
SJR quartileQ1
SJR score1.13
SNIP1.72
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TL;DR
An artificial neural network consisting of three neurons with nonlinear, positive and bounded response functions of the neurons is considered, which passes from stable to periodic and then chaotic regimes.
Abstract
An artificial neural network (ANN) consisting of three neurons has been considered. The equations of control are given by three differential equations (DE) with nonlinear, positive and bounded response functions of the neurons. Bifurcation diagram and three dimensional (3-D) phase portraits of the model show rich dynamics. With the change in synaptic weight and decay rate, the system passes from stable to periodic and then chaotic regimes. Interestingly, the system returns to periodic regime by further changing the synaptic weight. Computer code to calculate the Lyapunov exponent (LE) has been written to confirm chaos.
Keywords
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