Spiking neural networks based on a discrete second-order memristive synapse: Modeling, dynamics, and applications.

Discrete-time spiking neural networks provide an important framework for modeling discrete memristive synapses and for investigating their spike transmission and network dynamical behaviors. However, existing studies mostly focus on single-state discrete memristive synapses, and systematic research on second-order discrete memristive synapses in discrete-time spiking neural networks is still relatively scarce. Based on this, this paper constructs a second-order discrete memristive synapse model regulated by two internal-state variables in a coordinated manner. First, the basic dynamic characteristics of the proposed synapse model are analyzed, and its state evolution features and numerical stability performance under random spike input conditions are investigated. Subsequently, the model is embedded into a typical discrete neuron model for unified verification, and the results show that it can achieve stable pulse transmission. Furthermore, the influence of memristive synapse parameters and coupling strength on synchronization behavior is examined at the network level. The results indicate that the system can evolve from incomplete synchronization to high synchronization and exhibit chimera-like states in a ring-coupled network. Additionally, this paper conducts pulse coding, limited pattern discrimination, and spike-timing-dependent plasticity analysis based on the proposed synapse model. The results show that the model can maintain a certain information representation and pattern-discrimination ability under noise interference, providing a feasible solution for the stable modeling of memristive synapses and their information-processing applications in discrete spiking neural networks.