A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

doi:10.1088/1674-1056/19/4/040509

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.

Keywords: Hopfield neural network chaos bifurcation Lyapunov exponents

Received: 14 July 2009
Revised: 24 July 2009
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	02.30.Oz	(Bifurcation theory)
	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~60774088), the Program for New Century Excellent Talents in University of China (NCET), the Science \& Technology Research Key Project of Educational Ministry of China (Grant

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Chen Peng-Fei(陈鹏飞), Chen Zeng-Qiang(陈增强), and Wu Wen-Juan(吴文娟) A novel chaotic system with one source and two saddle-foci in Hopfield neural networks 2010 Chin. Phys. B 19 040509

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A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

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