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

作者：Chen Peng-Fei^*; Chen Zeng-Qiang; Wu Wen-Juan

来源：Chinese Physics B, 2010, 19(4): 040509.

DOI：10.1088/1674-1056/19/4/040509

• Hopfield neural network
• chaos
• bifurcation
• Lyapunov exponents

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.

• 出版日期2010-4
• 单位中国人民解放军军事交通学院; 南开大学