Multiscroll chaotic attractors and multistability in a ring of three coupled inertial Hopfield neurons: theoretical analysis and circuit simulation

Abstract

This paper studies the dynamics of three coupled inertial neurons-based system with hyperbolic tangent activation function. The model is described by a set of six coupled first order ODEs with odd symmetry and presents 27 equilibrium points some of which undergo multiple Hopf Bifurcations with the variation of a control parameter. Fascinating nonlinear features are revealed by the numerical investigations such as homogeneous and heterogeneous forms of multistability, eight-spiral chaotic attractors and oscillation death phenomenon. Phase portraits, bifurcation diagrams, frequency spectrum, spectrum of Lyapunov exponents and basins of attraction are produced to better highlight the various dynamic features. An analogue electronic circuit version of the three coupled inertial neuron system is designed and implemented in Orcad-PSpice software. PSpice simulation results verify the conclusions of the theoretical analysis.