Chaotic and Periodic Attractors in a Five-Dimensional Artificial Neural Network Model
Subject Areas : هندسه
1 - Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697 Tehran, Iran
Keywords: طیف لیاپونوف, ابرآشوب, آشوب, انشعاب دو برابر سازی دوره تناوب, آشوب گذرا,
Abstract :
In this article, the dynamics of a new model of Hopfield neural networks based on 5 neurons is presented and analyzed. In the synaptic coefficients of this model, two parameters are defined which, by changing them, very rich dynamic behaviors, including quasi-periodic attractors (3-torus), chaos, transient chaos, hyperchaos, period-doubling bifurcation route to chaos and coexistence attractors will be observed. This model will include almost most of the dynamic phenomena mentioned. In particular, we observe the period-doubling bifurcation leading to chaos, which has rarely been reported in previous works in five-dimensional autonomous systems, especially the Hopfield system. By changing the parameter a in a very small interval, the evolution process of the system starts from the limit cycle and after passing through a series of periodic attractors, it becomes chaotic. Complex dynamic behaviors of the system are investigated using the Lyapunov spectrum, bifurcation diagram and different sections of the phase space.
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