Influences of short-term and long-term plasticity of memristive synapse on firing activity of neuronal network

Synaptic plasticity can greatly affect the firing behavior of neural networks, and it specifically refers to changes in the strength, morphology, and function of synaptic connections. In this paper, a novel memristor model, which can be configured as a volatile and nonvolatile memristor by adjusting its internal parameter, is proposed to mimic the short-term and long-term synaptic plasticity. Then, a bi-neuron network model, with the proposed memristor serving as a coupling synapse and the external electromagnetic radiation being emulated by the flux-controlled memristors, is established to elucidate the effects of short-term and long-term synaptic plasticity on firing activity of the neuron network. The resultant seven-dimensional(7D) neuron network has no equilibrium point and its hidden dynamical behavior is revealed by phase diagram, time series, bifurcation diagram, Lyapunov exponent spectrum, and two-dimensional(2D) dynamic map. Our results show the short-term and long-term plasticity can induce different bifurcation scenarios when the coupling strength increases. In addition, memristor synaptic plasticity has a great influence on the distribution of firing patterns in the parameter space. More interestingly, when exploring the synchronous firing behavior of two neurons, the two neurons can gradually achieve phase synchronization as the coupling strength increases along the opposite directions under two different memory attributes. Finally, a microcontroller-based hardware system is implemented to verify the numerical simulation results.