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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40509-040509.doi: 10.1088/1674-1056/19/4/040509

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

陈增强¹, 吴文娟¹, 陈鹏飞²

(1)Department of Automation, Nankai University, Tianjin 300071, China; (2)Department of Automation, Nankai University, Tianjin 300071, China;The Institute of Military Transportation, Tianjin 300161, China

收稿日期:2009-07-14 修回日期:2009-07-24 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
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

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

Chen Peng-Fei(陈鹏飞)^a)b)^†, Chen Zeng-Qiang(陈增强)^a)^‡, and Wu Wen-Juan(吴文娟)^a)

^a Department of Automation, Nankai University, Tianjin 300071, China; ^b The Institute of Military Transportation, Tianjin 300161, China

Received:2009-07-14 Revised:2009-07-24 Online:2010-04-15 Published:2010-04-15
Supported by:
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

摘要/Abstract

摘要： 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.

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.

Key words: Hopfield neural network, chaos, bifurcation, Lyapunov exponents

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

02.30.Oz (Bifurcation theory) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

陈鹏飞, 陈增强, 吴文娟. A novel chaotic system with one source and two saddle-foci in Hopfield neural networks[J]. 中国物理B, 2010, 19(4): 40509-040509.

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[J]. Chin. Phys. B, 2010, 19(4): 40509-040509.

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

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

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