Numerical detection of stochastic to deterministic transition

TL;DR

This paper introduces a numerical method to detect the transition from stochastic to deterministic behavior in chemical oscillators by estimating a noise parameter that varies with system size.

Contribution

It proposes a novel noise parameter as an order parameter for identifying stochastic to deterministic transition in chemical systems, comparing different formalisms.

Findings

Noise parameter increases as system size decreases in stochastic regime.

In deterministic regime, noise parameter remains minimal regardless of system size.

Noise strength is smaller in Chemical Langevin equation compared to Master equation.

Abstract

We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from stochastic to deterministic regime. In stochastic regime, this noise parameter is found to be increased as system size decreases, whereas, in deterministic regime it remains constant to minimum value as system size increases. This let the transition from fluctuating to fixed limit cycle oscillation as the system goes from stochastic to deterministic transition. We also numerically estimated the strength of the noise parameter involved both in Chemical Langevin equation and Master equation formalisms and found that strength of this parameter is much smaller in the former than the later.