Synchronization, extreme multistability, and its control for a field coupled neurons with time delays

Abstract

Neurons are connected through synapses, but it is not reasonable to equate the connection mode of synapses to an edge in the network due to synaptic plasticity whereas the magnetic field coupling can be considered to handle it. Therefore, in this paper, the interaction between HR neurons is realized by magnetic field coupling based on induction coil, and time delay is introduced to represent the lag in information transfer. First, the coexisting firing activities and synchronization behaviors in dual neuronal networks are numerically calculated, respectively, depending on the external stimulation current, coupling strength, time delays, and initial conditions. When the time delays are given, it is interesting to note that the infinite number of firing modes including chaotic firing, periodical firing, and quiescent state is induced by initial conditions. Due to the initial values, the types of synchronization consisting of complete synchronization, delayed synchronization, and asynchronization are then revealed under the framework of extreme multistability. In particular, the state of complete synchronization exhibits only quiescent state and period-1 firing when the time delay is not equal to 0. Furthermore, the linear augmentation method is conceived to control extreme multistability. It can be found that the attractors with different positions and topological structures can be controlled to the point attractors with the same shape but with different positions when the coupling strength of linear system and nonlinear system is increased. That is, the heterogeneous multistability can be successfully controlled to the homogeneous multistability, and the coupled neurons can also be achieved synchronization after control. These conclusions in this paper could be helpful in providing new insights for studying neurodynamics and applying neural circuits.