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...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.展开更多
基金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)+1 种基金the Science & Technology Research Key Project of Educational Ministry of China(Grant No.107024)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin(Grant No.08JCZDJC21900)
文摘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.
