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Sensitivity analysis of the stochastically and periodically forced Brusselator

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  • Bashkirtseva, I.A
  • Ryashko, L.B

Abstract

The problem of sensitivity of nonlinear system limit cycle with respect to small stochastic and periodic disturbances is considered. Sensitivity analysis on the basis of quasipotential function is performed. The quasipotential is used widely in statistical physics (for instance by Graham for analysis of nonequilibrium thermodynamics problem). We consider an application of quasipotential technique to sensitivity problem. For the plane orbit case an approximation of quasipotential is expressed by some scalar function. This function (sensitivity function) is introduced as a base tool of a quantitative description for a system response on the external disturbances. New cycle characteristics (sensitivity factor, parameter of stiffness) are considered. The analysis of the forced Brusselator based on sensitivity function is shown. From this analysis the critical value of Brusselator parameter is found. The dynamics of forced Brusselator for this critical value is investigated. For small stochastic disturbances the burst of response amplitude is shown. For small periodic disturbances the period doubling regime of the transition to chaos scenario is demonstrated.

Suggested Citation

  • Bashkirtseva, I.A & Ryashko, L.B, 2000. "Sensitivity analysis of the stochastically and periodically forced Brusselator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 126-139.
    • Handle: RePEc:eee:phsmap:v:278:y:2000:i:1:p:126-139
    DOI: 10.1016/S0378-4371(99)00453-7
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    Cited by:

    1. 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.
    2. Bashkirtseva, Irina & Ryashko, Lev, 2017. "Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 573-584.
    3. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
    4. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
    5. Mandal, Partha Sarathi, 2018. "Noise-induced extinction for a ratio-dependent predator–prey model with strong Allee effect in prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 40-52.
    6. Bashkirtseva, I. & Ryashko, L., 2020. "Analysis of noise-induced phenomena in the nonlinear tumor–immune system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
    8. Bashkirtseva, Irina & Ryashko, Lev, 2013. "Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 295-306.

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