Synchronization in fractional-order neural networks by the energy balance strategy

Considering the individual differences between neurons, the fractional-order framework is introduced, and the neurons with various orders denote the individual differences during the cell differentiation. In this paper, the fractional-order FithzHugh-Nagumo (FHN) neural circuit is used to reproduce the firing patterns. In addition, an energy balance strategy is applied to determine the inter-neuronal communication. The neurons with energy imbalance exchange the information whereas the synaptic channels are blocked when energy balance is achieved. Two neurons coupled by this strategy achieve the phase synchronization and phase lock, and it indicates the two neurons generate spiking at the same time or with an interval. Similarly, the synchronization results are also obtained in the chain neuronal network, and the neurons exhibit the same firing patterns since the synchronization factor is closed to 1. Particularly, the neurons with order diversities lead to the heterogeneity and gradient field in the regular network, and the target wave is developed over time. With the wave spreading in the network, the silent states and exciting states appear in the whole network. The formation and diffusion of the target wave reveals the information transmission in neuronal network, and it indicates the individual differences paly an essential role in the collective behavior of neurons.