A plethora of behaviors in a memristor based Hopfield neural networks (HNNs)

Abstract

This work investigates the nonlinear dynamics of a model of memristor based Hopfield Neural Networks (HNNs). The investigations show that the memristive HNNs possesses three equilibrium points among which the origin and two nonzero equilibrium points. It is found that the origin and the nonzero equilibrium points are always unstable for the set of synaptic weights matrix used for the analysis. Numerical simulations, carried out in terms of bifurcation diagrams, graphs of Lyapunov exponents, phase portraits and frequency spectra, are used to highlight the complex dynamical behaviors exhibited by the model. The results indicate that the introduced memristive HNNs exhibits rich nonlinear dynamical behaviors including period doubling bifurcation, symmetry restoring crisis, chaos, periodic window, antimonotonicity (i.e. concurrent creation and annihilation of periodic orbits) and coexisting self-excited attractors (e.g. coexistence of two, four and six disconnected periodic and chaotic attractors) not reported in the relevant literature. Finally, PSpice simulation investigations support the results of theoretical analyses.