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 |
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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 |
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ISSN: | 0178-8051 1432-2064 |
DOI: | 10.1007/s00440-024-01301-4 |