Energy dependence of synchronization mode transitions in the delay-coupled FitzHugh-Nagumo system driven by chaotic activity.

Energy absorption and consumption are essential for the activity of single neurons and neuronal networks. The synchronization mode transition and energy dependence in a delay-coupled FitzHugh-Nagumo (FHN) neuronal system driven by chaotic activity are investigated in this paper. With the change of chaotic current intensity, it was found that the synchronization mode of coupled neurons undergoes synchronous state, transition state, anti-phase state, alternating asynchronous and anti-phase state, and chaotic current-induced chaotic state. The Hamiltonian energy is much dependent on the synchronization mode of coupled neurons. The synchronization mode and the Hamiltonian energy of coupled neurons can be modulated by chaotic current intensity, coupling strength and time delay. The introduction of the time delay induces the system to become bistable state. Chaotic current as an external force induced transitions between the synchronous and anti-phase states. Coupling strength is an intrinsic property of the system and can change the properties of the bistable state. Furthermore, the synchronous and anti-phase states appear intermittently with the increasing of time delay. A chained neuronal network is used to prove that the synchronization mode transition of the system of multiple neurons is similar to the two neurons. The results of this paper might help one to understand the intrinsic energy alteration mechanisms of neuronal synchronization.