Effect of electromagnetic radiations on the dynamics of a five-chain coupled inertial Hopfield neural network and control of multi-stability with the selection of a desired attractor

Abstract In this paper, we investigate the effect of electromagnetic radiation on the dynamics of a network consisting of five chain-coupled inertial Hopfield neurons. The study revealed that the neural system designed such a way involves several complex phenomena, namely Hopf bifurcation, chaos, hyperchaos and the coexistence of up to thirty-two attractors in phase space. The complexity specific to our system is due to the higher number of equilibrium points, namely two hundred and forty-three. Under the conditions of safe functioning of our neural system (chaos or hyperchaos), we have been able to observe that electromagnetic radiation has a harmful character for the system, because we found for a range of variation in the intensity of the electromagnetic feedback induction current a coexistence of chaotic and periodic states (epileptic state). We then controlled the multi-stability using a desired attractor selection scheme, with the aim of suppressing the pathological state. All the work carried out in this contribution is done with the help of dynamical system analysis tools such as the bifurcation diagram, the spectrum and the maximum exponent of Lyapunov, phase portraits and basins of attraction. The numerical scheme used is the Runge–Kutta-4. In order to validate the numerical results, we use analog calculation and some results were derived from the PSpice software. These results are in good accordance in amplitude and location on the plane to those of numerical simulations.