Modeling of memristor-based Hindmarsh-Rose neuron and its dynamical analyses using energy method.

• The HR neuron model with one parameter's memristor is proposed and its hidden dynamics is studied. • The generalized Hamiltonian function is derived completely and reveals the mechanism of firing of neuron. • The positive effects of noise on electrical activities are found in the improved MHR neuron. It has been extensively studied to employ memristors to model the relationship between the electromagnetic field and the membrane potential, especially for the research of modeling and dynamical analyses of electrical activity using HR neurons with memristors. This paper proposes a novel 4D HR model with a threshold flux-controlled memristor (MHR), which describes the electromagnetic induction effect. The proposed 4D HR model retains the original HR properties and can describe the complex dynamics of neurons' electrical activities with fewer parameters than the existing models. Due to the particularity of the no equilibrium point of the MHR model, the hidden dynamics are found in the proposed MHR model. The generalized Hamiltonian function is fully derived for the MHR neuron model using Helmholtz's theorem. The simplest form of the Hamiltonian form is given by assigning special values. The average Hamiltonian energy and its bifurcation are employed to find the connection between energy and firing patterns. The band-limited white noise is also studied, and it is found that it positively influences the electrical activities in the proposed MHR system. [ABSTRACT FROM AUTHOR]