An adaptive synchronization approach in a network composed of four neurons with energy diversity

Due to the diversity in excitability and some intrinsic parameters, these neurons present different firing patterns and energy diversity becomes distinct. As a result, flexible synapses are guided to connect neurons clustered in the same region for generating fast synchronous firing patterns, and then energy balance is stabilized between neurons. In this work, four FitzHugh-Nagumo (FHN) neurons in chain network and ring network are connected via memristive synapses, and the collective neural activities are controlled by taming the memristive coupling adaptively via Heaviside function, which the coupling intensity is increased exponentially to reaches a saturation value under complete synchronization and energy balance between neurons. Bifurcation analysis, Lyapunov exponent spectrum and Hamilton energy for single neuron are calculated to find dynamics dependence on external stimulus and parameters. The Heaviside function terminates the increase in coupling intensity when energy diversity between adjacent neurons is decreased to a tiny value, which means reaching local energy balance in the neural network. The error function, phase error and energy error are used to explore the collective behaviors of network during the adaptive energy propagation. It is found that identical neurons can reach complete synchronization and energy balance well while the nonidentical neurons can reach phase lock and firing patterns become unstable even under energy balance. This discussion provides a clue to understand the biophysical mechanism for control of synapse growth in the network under energy flow, and external energy injection can be effective to control the neural networks.

Automated summary

Due to the diversity in excitability and intrinsic parameters, neurons present different firing patterns and energy diversity. In this work, four FHN neurons in chain and ring networks are connected via memristive synapses, and their collective activities are controlled by adaptively taming the memristive coupling. Bifurcation analysis, Lyapunov exponent spectrum and Hamilton energy are calculated to investigate the dynamics dependence on external stimulus and parameters.