Multistable Dynamics in a Hopfield Neural Network Under Electromagnetic Radiation and Dual Bias Currents

Abstract

This paper investigates a Hopfield neural network (HNN) under the simulation of external electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux across the neuron membrane is used to emulate the influence of electromagnetic radiation. Utilizing conventional analytical methods, the basic properties of the proposed Hopfield neural network are discussed. Due to the addition of electromagnetic radiation and dual bias currents, the Hopfield neural network shows high sensitivity to system parameters and initial conditions. The proposed Hopfield neural network possesses multistability with periodic attractor, quasi-periodic attractor, chaotic attractor and transient chaotic attractor, and all of the attractors are hidden attractors because there is no equilibrium point in the system. In particular, when the neuron membrane magnetic flux is different, the system can present transient chaos with different chaotic times. More interestingly, with the change of system parameters, the proposed Hopfield neural network can exhibit parallel bifurcation behaviors. Finally, the Multisim simulation and hardware experiment results based on discrete electronic components are conducted to support the numerical ones. These results could give useful information to the study of nonlinear dynamic characteristics of the Hopfield neural network.

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

“…Experiments [5,6] showed that the nervous system exhibited high synchronization during seizures. In order to better understand the structure of the brain, researchers have studied a large number of dynamic characteristics of neural networks [7][8][9][10][11][12]. However, continuous neuron models have the characteristics of high dimension and multiscale, which are not conducive to the study of complex and large-scale neural networks.…”