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Stochastic Hopf bifurcation in a biased van der Pol model

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  • Leung, H.K.

Abstract

The transient characteristics of a nonequilibrium phase transition is investigated in a model of abiased van der Pol oscillator. The state-independent driving term which triggers the bifurcation from limit cycle to fixed point is treated as a randomly fluctuating quantity. The advancement of the Hopf bifurcation is explained as a result of noise-induced periodicity found in this model system. The phase boundary separating the two attractors is determined numerically and is interpreted as stochastic bifurcation locus in parameter space. The phenomenon of critical slowing down occurring on the fixed point side is found to be similar to that which occurs in a deterministic system. The relevent critical exponent is estimated to have the mean field value of unity, irrespective of how the stochastic bifurcation points are approached in a two-dimensional parameter space.

Suggested Citation

  • Leung, H.K., 1998. "Stochastic Hopf bifurcation in a biased van der Pol model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 146-155.
    • Handle: RePEc:eee:phsmap:v:254:y:1998:i:1:p:146-155
    DOI: 10.1016/S0378-4371(98)00017-X
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    Cited by:

    1. He, Qun & Xu, Wei & Rong, Haiwu & Fang, Tong, 2004. "Stochastic bifurcation in Duffing–Van der Pol oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 319-334.
    2. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    3. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
    4. Martiny, Emil S. & Jensen, Mogens H. & Heltberg, Mathias S., 2022. "Detecting limit cycles in stochastic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

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