Physical characteristic and dynamics in a neural circuit without using inductor and nonlinear resistor

Neural circuits can be adjusted to produce similar electrical activities as in biological neurons. During propagation of ions and exchange of charges, emergence of electric field is accompanied with changes of magnetic flux, and field energy is shunted and converted between magnetic field and electric field. Continuous oscillation in nonlinear circuit depends on the incorporation of nonlinear device, capacitive and inductive components by exchanging energy between inductor and capacitor. In this work, a simple memristor-coupled neural circuit is designed to propose a double capacitive neuron model without incorporating inductor and nonlinear resistor into the nonlinear circuit. Energy function for the memristive neuron is defined and its regulation on intrinsic parameter and dynamics is discussed in detail, and chaos is induced. Systematic stability analysis discovered a close relationship between chaotic solutions and strange attractors. Indeed, incorporation of any two of the three fundamental components including resistor (R), inductor (L), and capacitor (C) is sufficient to generate complex dynamical behaviors. Notably, the energy level of periodic states is higher than that of chaotic states, highlighting the crucial role of energy in mode transitions. Applying noisy excitation on memristive channels and membrane variables, stochastic resonance is induced. The energy in memristive channel is estimated and used to control one bifurcation parameter, and mode transition is controlled in adaptive way. It provides clues to clarify the physical characteristic of neural circuit and has potential application in encoding signals in nervous system.