Collective behaviors of fractional-order FithzHugh–Nagumo network

Abstract

Brain connection is the mechanism of determining the brain function and cognition, and the small world network is widely investigated among these connections. In this paper, the small world complex brain network is constructed by the fractional-order neurons, and the fractional-order memristor is used to connect these neurons. Compared with the integer-order counterpart, the fractional-order memristor describes precisely the distortion of hysteresis curves, and it exhibits more abundant dynamical behaviors to function as the synapse. In addition, the neurons with different fractional orders represent the individual differences during the cell differentiation. For the two coupled neurons, the phase lock is achieved in the bursting and spiking neurons, and it denotes a time delay between the two firing process, whereas the chaotic neurons cannot synchronize. In small world network, the collective behaviors of neurons tend to synchronize with the increasing of the coupling intensity. These results promote the understanding of information coding and transformation in complex brain network.