Dynamical Behaviors in Discrete Memristor-Coupled Small-world Neuronal Networks

Abstract

Brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other. The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity. In this paper, a memristor is used to simulate synapse, and a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored. We explore the influence of system parameter on the dynamical behaviors of the discrete small-world network, and the system shows a variety of firing patterns such as spiking firing and triangular bursting firing when the neuronal parameter α is changed. The numerical simulation results based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network, and the higher the reconnection probability, the number of nearest neurons, and the more significant the synchronization state of neurons. In addition, by increasing the coupling strength of memristor synapses, synchronization performance is promoted. The results of this paper can boost the research process of complex neuronal networks coupled with memristor synapse and further promote the development of neuroscience.