Lyapunov exponents and shear-induced chaos for a Hopf bifurcation with additive noise

This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior of the top Lyapunov exponent $$\lambda $$ λ associated with this random dynamical system as one or more of the parameter...

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Veröffentlicht in:Probability theory and related fields 2024-07
1. Verfasser: Baxendale, Peter H.
Format: Artikel
Sprache:eng
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Zusammenfassung:This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior of the top Lyapunov exponent $$\lambda $$ λ associated with this random dynamical system as one or more of the parameters in the system tend to 0 or $$\infty $$ ∞ . This enables the construction of a bifurcation diagram in parameter space showing stable regions where $$\lambda 0$$ λ > 0 (implying chaotic behavior). The value of $$\lambda $$ λ depends strongly on the shearing effect of the twist factor b / a of the deterministic Hopf bifurcation. If b / a is sufficiently small then $$\lambda
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-024-01301-4