Defects formation and wave emitting from defects in excitable media

Abstract

Abnormal electrical activities in neuronal system could be associated with some neuronal diseases. Indeed, external forcing can cause breakdown even collapse in nervous system under appropriate condition. The excitable media sometimes could be described by neuronal network with different topologies. The collective behaviors of neurons can show complex spatiotemporal dynamical properties and spatial distribution for electrical activities due to self-organization even from the regulating from central nervous system. Defects in the nervous system can emit continuous waves or pulses, and pacemaker-like source is generated to perturb the normal signal propagation in nervous system. How these defects are developed? In this paper, a network of neurons is designed in two-dimensional square array with nearest-neighbor connection type; the formation mechanism of defects is investigated by detecting the wave propagation induced by external forcing. It is found that defects could be induced under external periodical forcing under the boundary, and then the wave emitted from the defects can keep balance with the waves excited from external forcing.