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

This paper presents the finding of a novel chaotic systemwith one source and two saddle-foci in a simple three-dimensional(3D) autonomous continuous time Hopfield neural network. Inparticular, the system with one source and two saddle-foci has achaotic attractor and a periodic attractor with different initialpoints, which has rarely been reported in 3D autonomous systems. Thecomplex dynamical behaviours of the system are further investigatedby means of a Lyapunov exponent spectrum, phase portraits andbifurcation analysis. By virtue of a result of horseshoe theory indynamical systems, this paper presents rigorous computer-assistedverifications for the existence of a horseshoe in the system for acertain parameter.