Synchronization and patterns in a memristive network in noisy electric field

A simple neural circuit coupled by magnetic flux-controlled memristor (MFCM) can be controlled to describe the electromagnetic effect and radiation on biological neurons. In this paper, the effect of external electric field on biophysical neurons is identified by adding a charge-controlled memristor into a nonlinear circuit. This memristive circuit can present a variety of firing patterns by tuning the angular frequency of an external voltage source. As a result, the physical field energy in this neural circuit and its equivalent Hamilton energy for memristive neuron are dependent on the firing modes of neural activities. For clustered neurons, field energy is exchanged and propagated to obtain fast energy balance by regulating the charge flow in the chain network. Indeed, the growth of coupling intensity is controlled by the energy difference between adjacent neurons, and perfect energy balance keeps a saturation value for coupling intensity. The collective behaviors of memristive neurons in the chain network are adjusted by regulating the coupling intensity for the exchange of charges. In addition, noisy disturbance from external electric field is applied to study the synchronization stability and wave propagation in the network, and energy flow is estimated. Graphical abstract A simple neural circuit coupled by magnetic flux-controlled memristor (MFCM) can be controlled to describe the electromagnetic effect and radiation on biological neurons. In this paper, the effect of external electric field on biophysical neurons is identified by adding a charge-controlled memristor into a nonlinear circuit. This memristive circuit can present a variety of firing patterns by tuning the angular frequency of an external voltage source. As a result, the physical field energy in this neural circuit and its equivalent Hamilton energy for memristive neuron are dependent on the firing modes of neural activities. For clustered neurons, field energy is exchanged and propagated to obtain fast energy balance by regulating the charge flow in the chain network. Indeed, the growth of coupling intensity is controlled by the energy difference between adjacent neurons, and perfect energy balance keeps a saturation value for coupling intensity. The collective behaviors of memristive neurons in the chain network are adjusted by regulating the coupling intensity for the exchange of charges. In addition, noisy disturbance from external electric field is applied to study the synchronization stability and wave propagation in the network, and energy flow is estimated.