Energy and synchronization between two neurons with nonlinear coupling.

Consensus and synchronous firing in neural activities are relative to the physical properties of synaptic connections. For coupled neural circuits, the physical properties of coupling channels control the synchronization stability, and transient period for keeping energy diversity. Linear variable coupling results from voltage coupling via linear resistor by consuming certain Joule heat, and electric synapse coupling between neurons derives from gap junction connection under special electrophysiological condition. In this work, a voltage-controlled electric component with quadratic relation in the - (current-voltage) is used to connect two neural circuits composed of two variables. The energy function obtained by using Helmholtz theorem is consistent with the Hamilton energy function converted from the field energy in the neural circuit. Chaotic signals are encoded to approach a mixed signal within certain frequency band, and then its amplitude is adjusted to excite the neuron for detecting possible occurrence of nonlinear resonance. External stimuli are changed to trigger different firing modes, and nonlinear coupling activates changeable coupling intensity. It is confirmed that nonlinear coupling behaves functional regulation as hybrid synapse, and the synchronization transition between neurons can be controlled for reaching possible energy balance. The nonlinear coupling is helpful to keep energy diversity and prevent synchronous bursting because positive and negative feedback is switched with time. As a result, complete synchronization is suppressed and phase lock is controlled between neurons with energy diversity.