A novel chaotic system with one source and two saddle-foci in Hopfield neural networks |
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Authors: | Chen Peng-Fei Chen Zeng-Qiang and Wu Wen-Juan |
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Institution: | Department of Automation, Nankai University, Tianjin 300071, China; The Institute of Military Transportation, Tianjin 300161, China |
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Abstract: | This paper presents the finding of a novel chaotic system
with one source and two saddle-foci in a simple three-dimensional
(3D) autonomous continuous time Hopfield neural network. In
particular, the system with one source and two saddle-foci has a
chaotic attractor and a periodic attractor with different initial
points, which has rarely been reported in 3D autonomous systems. The
complex dynamical behaviours of the system are further investigated
by means of a Lyapunov exponent spectrum, phase portraits and
bifurcation analysis. By virtue of a result of horseshoe theory in
dynamical systems, this paper presents rigorous computer-assisted
verifications for the existence of a horseshoe in the system for a
certain parameter. |
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Keywords: | Hopfield neural network chaos bifurcation Lyapunov
exponents |
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