Chaos and Synchronization in a Memristor-Coupled HR-FN Neuron

Artificial neural networks are commonly employed to mimic biological activities in the brain. Synapse as the neuron connecter plays an important role in information transmission, which revises the dynamics of coupled neurons inevitably or even bring synchronization behavior. In this work, by coupling the FitzHugh-Nagumo neuron (FN) and Hindmarsh-Rose neuron (HR) with a memristor synapse, a 5D neuron system is derived. The dynamics and synchronization feature of the coupled memristive neuron including period-doubling bifurcation and chaotic bursting were exhaustively studied through phase portraits, Lyapunov exponents, and bifurcation diagrams. It shows that the coupling strength of the synapse poses a great impact on the evolution of membrane potential including phase synchronization and complete synchronization. In addition, the derived HR-FN Neuron has the property of offset boosting and local frequency control. Offset boosting poses unique effects on synchronization when the derived neuron exhibits different firing dynamics.