Dynamics of a modified Hindmarsh–Rose neural model with random perturbations: Moment analysis and firing activities

Argha Mondal and Ranjit Kumar Upadhyay

Physica A: Statistical Mechanics and its Applications, 2017, vol. 486, issue C, 144-160

Abstract: In this paper, an attempt has been made to understand the activity of mean membrane voltage and subsidiary system variables with moment equations (i.e., mean, variance and covariance’s) under noisy environment. We consider a biophysically plausible modified Hindmarsh–Rose (H–R) neural system injected by an applied current exhibiting spiking–bursting phenomenon. The effects of predominant parameters on the dynamical behavior of a modified H–R system are investigated. Numerically, it exhibits period-doubling, period halving bifurcation and chaos phenomena. Further, a nonlinear system has been analyzed for the first and second order moments with additive stochastic perturbations. It has been solved using fourth order Runge–Kutta method and noisy systems by Euler’s scheme. It has been demonstrated that the firing properties of neurons to evoke an action potential in a certain parameter space of the large exact systems can be estimated using an approximated model. Strong stimulation can cause a change in increase or decrease of the firing patterns. Corresponding to a fixed set of parameter values, the firing behavior and dynamical differences of the collective variables of a large, exact and approximated systems are investigated.

Keywords: Modified H–R system; Stability; Bifurcation; White noise; Moment equations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:486:y:2017:i:c:p:144-160

DOI: 10.1016/j.physa.2017.05.086

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