Creation of heterogeneity or defects in a memristive neural network under energy flow

The field energy in neuron can be changed under shape deformation because of external energy injection into the media. The electromagnetic field superposition enables energy pumping when neurons in the same region are stimulated, and synaptic connection can be created adaptively for keeping local energy balance. All neurons will keep energy balance with the adjacent neurons in the network by continuous energy propagation and exchange, and identical neurons will develop a homogeneous state while non-identical neurons will support formation of gradient spatial patterns. In this paper, the simple Fitzhugh–Nagumo (FHN) neural circuit is improved by incorporating a thermistor and a phototube in different branch circuits synchronously, and this neuron becomes sensitive to light and temperature. The Hamilton energy for this functional neuron is obtained to discern the dependence of firing modes on the energy level. These functional neurons are clustered to build a regular network via memristive synapses, and the creation and growth of memristive synapse can be controlled by energy diversity between adjacent neurons. It is found that heterogeneity in the network can be formed when more energy is accumulated locally, while the occurrence of local defects results from energy release and lower energy in a local area. As a result, shape deformation occurs and some parameters for the neurons covered with heterogeneity or defects show certain changes with time. The collective behaviors of the network are investigated by calculating the membrane potentials for neurons, Hamilton energy, coupling intensity and synchronization factor. The results indicate that energy diversity between neurons controls the occurrence of heterogeneity and defects in the network and local energy injection can control the firing patterns of network because the wave propagation can be regulated by the heterogeneity and defects.