Hidden and self-excited firing activities of an improved Rulkov neuron, and its application in information patterns

Information patterns in a neuron model describe the possible modes in which information is processed and transmitted within neurons and neural networks. An improved Rulkov neuron with the aim of revealing its unexplored dynamics is introduced and investigated, with possible application to information coding carried out in this work. After introducing the neuron model, its stability around the single equilibrium point is examined, and it is discovered that the system is able to exhibit both stable and unstable dynamics. Using two-parameter charts, the system’s global stability dynamics are obtained, and windows of the hidden and self-excited dynamics involving both chaotic and periodic states are clearly separated. For the validation of the result of the mathematical model, an electronic circuit was developed in Pspice simulation environment, and both results were in good accord. Finally, a network of 500 improved Rulkov neurons under the chain configuration is used to explore the phenomenon of the information patterns. From that investigation, it was found that the improved Rulkov neural lattice under modulational instability presents repetitive, regular stripes of bright and dark bands that are almost periodic and localized in space and time related to synchronization. These results could provide guidance in discerning information processing patterns in the nervous system.