Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons

Abstract

Spiral waves have been reported to be existent in the neocortex, during pharmacologically induced oscillations and sleep-like states. In the last decades, theoretical studies have demonstrated an underlying mechanism of the generation of spiral waves in a heart system. Nevertheless, how can a neural system produce spontaneous spiral wave and whether this behavior is sensitive to the dynamics of isolated neurons have not been systematically studied yet. In this paper we propose a modified Hindmarsh-Rose (HR) neuron model to study whether spiral wave can occur spontaneously in a two-dimensional array of HR neurons, which evolves from the initial state with a random phase distribution. The simulation results show that whether spiral wave can occur spontaneously in the system depends on the state of the single HR neuron, initial state of system and coupling strength. Especially, the state of the single HR neuron plays a central role. When the single HR neuron is in the state of period 1 spike, multiple spiral waves and spiral pairs can be generated spontaneously in the system for a certain range of coupling strength. In this case, the formations of spiral waves are completely independent of the initial state of the system, and as long as choosing an appropriate coupling strength, a single spiral wave can be found in the system. Furthermore, when the coupling strength exceeds a certain threshold value, the system will exhibit three kinds of dynamical behaviors, and correspond to three kinds of the different initial states, respectively. When system evolves from the first kind of initial state, the single spiral wave can be found occasionally in the system. When the system evolves from the second or third kind of initial state, the oscillation with intermittently global synchronization and oscillation death can be observed in the system, respectively. When a single HR neuron is in the state of period 2 spike, the spiral wave can appear spontaneously in the system only when the phase distribution of the initial state approaches to a uniform distribution. Moreover, the range of coupling strength on the generation of spiral wave is smaller than that of period 1 spike. When the single HR neuron is in a higher periodic state, it is difficult to generate spontaneously spiral wave in the system. These results are useful in understanding the spontaneous generation of spiral waves in the neocortex.