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Stochastic chaos in chemical Lorenz system: Interplay of intrinsic noise and nonlinearity

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  • Thounaojam, Umeshkanta Singh

Abstract

In this paper, we address the question of whether the phenomenon of chaos can occur in a purely stochastic system or not. We show that chaos can arise in a purely stochastic chemical Lorenz system. A robust regime of stochastic chaos develops like the onset of chaos in a deterministic system. Stochastic trajectories, which are initially very close, show sensitivity to initial states where they diverge exponentially as time progress. The interplay of nonlinearity and intrinsic noise in the chemical Lorenz system is studied to understand the effect of intrinsic noise. We observe that intrinsic noise can destabilize the fixed points and limit cycle attractors where stochastic trajectories make excursions along the unstable manifold, giving rise to the noisy chaotic attractors. This study uses quantitative measures like power spectrums and invariant measures to characterize the strange noisy attractors. Our study establishes that the interplay of intrinsic noise and nonlinearity gives rise to chaos in the stochastic Lorenz system.

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  • Thounaojam, Umeshkanta Singh, 2022. "Stochastic chaos in chemical Lorenz system: Interplay of intrinsic noise and nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009420
    DOI: 10.1016/j.chaos.2022.112763
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    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    2. William J. Blake & Mads KÆrn & Charles R. Cantor & J. J. Collins, 2003. "Noise in eukaryotic gene expression," Nature, Nature, vol. 422(6932), pages 633-637, April.
    3. Christopher V. Rao & Denise M. Wolf & Adam P. Arkin, 2002. "Control, exploitation and tolerance of intracellular noise," Nature, Nature, vol. 420(6912), pages 231-237, November.
    4. Mikhaylov, A.N. & Guseinov, D.V. & Belov, A.I. & Korolev, D.S. & Shishmakova, V.A. & Koryazhkina, M.N. & Filatov, D.O. & Gorshkov, O.N. & Maldonado, D. & Alonso, F.J. & Roldán, J.B. & Krichigin, A.V. , 2021. "Stochastic resonance in a metal-oxide memristive device," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Filatov, D.O. & Koryazhkina, M.N. & Novikov, A.S. & Shishmakova, V.A. & Shenina, M.E. & Antonov, I.N. & Gorshkov, O.N. & Agudov, N.V. & Carollo, A. & Valenti, D. & Spagnolo, B., 2022. "Effect of internal noise on the relaxation time of an yttria stabilized zirconia-based memristor," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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