Coexistence and control of firing patterns in a heterogeneous neuronal network coupled by memristive synapses

Abstract

To simulate the complex electrical activity exhibited in biological neuronal networks more accurately, a heterogeneous neuron-coupled network is established in this study. This network consists of an Hindmarsh-Rose (HR) neuron and a tri-cell Hopfield Neural Network (HNN) interconnected via three memristive synapses. The complex dynamical behaviors of the heterogeneous coupled network are investigated by means of bifurcation diagram, Lyapunov exponent, time series and phase portrait. The firing pattern transitions are also revealed as the memristive synaptic coupling strengths vary. Furthermore, coexisting firing patterns, including period-1, period-2, period-4 and chaotic firing, are also observed by manipulating the initial conditions. Especially, a linear augmentation strategy is introduced to target a desired firing pattern. Both numerical simulations and hardware experimental tests demonstrate that the linear augmentation method can not only select the desired firing patterns, but also promote synchronous firing activities within the heterogeneous neuronal network.