Initial condition-offset regulating synchronous dynamics and energy diversity in a memristor-coupled network of memristive HR neurons

Memristors can be thought of as special connection synapses with internal states that regulate synchronous behavior or energy propagation between neurons in a neural network. By connecting two memristive Hindmarsh-Rose (mHR) neurons with one memristor coupling, this paper synthesizes a memristor-coupled mHR neuron (MC-mHRN) network without equilibrium point. For this network, the synchronization condition regulated by the initial condition-offset (ICO) of the memristive channel are derived theoretically, and the ICO-regulating synchronous dynamics is evaluated numerically. Furthermore, the Hamiltonian energy of mHR neuron is studied by Helmholtz's theorem, and the ICO-regulating energy diversity is analyzed numerically. It is demonstrated that the coupling strength and initial condition of the memristive channel can regulate the synchronous dynamics and energy diversity in the MC-mHRN network, thus achieving complete synchronization as well as energy balance. Consequently, the two mHR neurons in hidden chaotic firing modes deliver field energy via memristive channel until the fully synchronized energy balance is achieved. In addition, a digital platform of the MC-mHRN network is fabricated, and the experimental results validate the numerical ones of the synchronous dynamics.