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Bifurcations in Asymptotically Autonomous Hamiltonian Systems Subject to Multiplicative Noise

Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O., 29, Saint Petersburg, 199178, Russia

https://doi.org/10.1142/S0218127422501644Cited by:2 (Source: Crossref)

Abstract

The effect of multiplicative stochastic perturbations on planar Hamiltonian systems is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates bifurcations associated with changes in the stability of the equilibrium and with the appearance of new stochastically stable states in the perturbed system. It is shown that depending on the structure and the parameters of the decaying perturbations, the equilibrium can remain stable or become unstable. In some intermediate cases, a practical stability of the equilibrium with estimates for the length of the stability interval is justified. The performed stability analysis is based on a combination of the averaging method and the construction of stochastic Lyapunov functions.

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References

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