Chaotic dynamics in a neural network with different types of external stimuli

Abstract

Biological nervous system is very sensitive to external disturbances, and appropriate stimulus is beneficial for improving neural function in the neural system. In this paper, the effect of different external stimuli on chaotic dynamics in a Hopfield neural network with three neurons is explored. Mathematical model of the neural network is respectively established under three different cases, namely without external stimulus, with only electromagnetic radiation stimulus, and with both electromagnetic radiation stimulus and multi-level-logic pulse stimulus. Under the three cases, equilibrium points, stabilities, and attractors of the neural network are investigated carefully. The research results demonstrate that the neural network with periodic attractors can induce abundant chaotic attractors by imposing electromagnetic radiation on its one neuron. And when this neuron is simultaneously stimulated via electromagnetic radiation and multi-level-logic pulse, the neural network can produce complex multi-scroll attractors previously unobserved in Hopfield-type neural networks. Numerical results are verified by hardware experiments, effectively. Furthermore, based on the Helmholtzâs theorem, the Hamilton energy of the neural network is calculated and analyzed. It is found that lower average Hamilton energy can be detected in the neural network when complexity of external stimuli is enhanced. These new findings could offer a new insight into the occurrence mechanism of some neurological diseases.