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Research Papers

Numerical Detection of Stochastic to Deterministic Transition

[+] Author and Article Information
R. K. Brojen Singh

School of Computational
and Integrative Sciences,
Jawaharlal Nehru University,
New Delhi 110067, India;
Centre for Interdisciplinary Research in
Basic Sciences,
Jamia Millia Islamia,
New Delhi 110025, India
e-mail: brojen@mail.jnu.ac.in

Manuscript received September 16, 2011; final manuscript received April 8, 2014; published online September 12, 2014. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 10(1), 011001 (Sep 12, 2014) (5 pages) Paper No: CND-11-1154; doi: 10.1115/1.4027441 History: Received September 16, 2011; Revised April 08, 2014

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 latter.

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Figures

Grahic Jump Location
Fig. 1

The plots of the dynamics of X, Y, and Z at three different system sizes, V = 1, 100, and 1000, respectively, simulated using Gillespie's SSA [3]. The parameters used are same as is used in Gillespie [3].

Grahic Jump Location
Fig. 2

The plots showing the estimation of noise parameter in amplitudes for X and Y variables. The left panels show the transition from fluctuating to fixed limit cycle oscillation as the function of V, as V goes from small (stochastic regime) to large V (deterministic regime). The right panels show the phase plot in (ηA, V) plane indicating stochastic and deterministic regimes.

Grahic Jump Location
Fig. 3

The plots of ηLX and ηLY as a function of V both for CLE by simulating Eq. (5) and ME by simulating reactions (3) using SSA

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