Abstract
The phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network. A general mean field coupling is proposed to model the neuronal interactions. A standard order parameter is defined for quantifying the network dynamics. Investigations are undertaken for both the noise free network as well as stochastic networks, where the interneuronal coupling strength is assumed to be superimposed with additive noise. The existence of both smooth and explosive AT are observed in the parameter space for both the noise free and the stochastic networks. The effects of noise on AT are investigated and are found to play a constructive role in mitigating the effects of inactive neurons and reducing the parameter regime in which explosive AT is observed.
Highlights
The phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network
The phenomenon of explosive AT in an ER network of coupled Rulkov neurons has been studied, with network connectivity, coupling strength and the fractional ratio of inactive neurons being the parameters of interest
This has been investigated for both the noise free network as well as the stochastic network
Summary
The phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network. An order parameter, which is a measure of the collective dynamical characteristic of a complex network in which the individual components can behave quite differently, is defined to qualitatively and quantitatively investigate the parameter regimes at which these ageing transitions are observed. A mean field coupling model is proposed for the neuronal interconnections and the conditions for AT are investigated using measures based on standard order parameters. The network dynamics is governed by an intricate interplay between the four parameters gm , D, Pd and Pn. To quantify the collective dynamical characteristics of the network, an order parameter A is defined, which is a normalised measure for the largest amplitude of the oscillations in the steady state condition averaged across all neurons in the network; see Eqs. A can take values between unity and zero, with zero indicating that none of the neurons are oscillating and the network collectively becomes inactive (or dead)
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