Energy-guided synapse coupling between neurons under noise

From a physical viewpoint, any external stimuli including noise disturbance can inject energy into the media, and the electric response is regulated by the equivalent electric stimulus. For example, mode transition in electric activities in neurons occurs and kinds of spatial patterns are formed during the wave propagation. In this paper, a feasible criterion is suggested to explain and control the growth of electric synapse and memristive synapse between Hindmarsh-Rose neurons in the presence of noise. It is claimed that synaptic coupling can be enhanced adaptively due to energy diversity, and the coupling intensity is increased to a saturation value until two neurons reach certain energy balance. Two identical neurons can reach perfect synchronization when electric synapse coupling is further increased. This scheme is also considered in a chain neural network and uniform noise is applied on all neurons. However, reaching synchronization becomes difficult for neurons in presenting spiking, bursting, and chaotic and periodic patterns, even when the local energy balance is corrupted to continue further growth of the coupling intensity. In the presence of noise, energy diversity becomes uncertain because of spatial diversity in excitability, and development of regular patterns is blocked. The similar scheme is used to control the growth of memristive synapse for neurons, and the synchronization stability and pattern formation are controlled by the energy diversity among neurons effectively. These results provide possible guidance for knowing the biophysical mechanism for synapse growth and energy flow can be applied to control the synchronous patterns between neurons.