Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

Longo, Iacopo P.; Obaya, Rafael; Sanz, Ana M.

doi:10.1016/j.jde.2024.09.011

Journal of Differential Equations

2025

DOI: 10.1016/j.jde.2024.09.011

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Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

Iacopo P. Longo,

Rafael Obaya,

Ana M. Sanz

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Cited by 1 publication

References 14 publications

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On the transition between autonomous and nonautonomous systems: The case of FitzHugh–Nagumo’s model

Longo,

Queirolo,

Kuehn

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This work deals with a parametric linear interpolation between an autonomous FitzHugh–Nagumo model and a nonautonomous skewed problem with the same fundamental structure. This paradigmatic example allows us to construct a family of nonautonomous dynamical systems with an attracting integral manifold and a hyperbolic repelling trajectory located within the nonautonomous set enclosed by the integral manifold. Upon the variation of the parameter the integral manifold collapses, the hyperbolic repelling solution disappears and a unique globally attracting hyperbolic solution arises in what could be considered yet another pattern of nonautonomous Hopf bifurcation. Interestingly, the three phenomena do not happen at the same critical value of the parameter, yielding, thus, an example of a nonautonomous bifurcation in two steps. We provide a mathematical description of the dynamical objects at play and analyze the periodically forced case via rigorously validated continuation.

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On the transition between autonomous and nonautonomous systems: The case of FitzHugh–Nagumo’s model

Longo,

Queirolo,

Kuehn

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

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Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

Cited by 1 publication

References 14 publications

On the transition between autonomous and nonautonomous systems: The case of FitzHugh–Nagumo’s model

On the transition between autonomous and nonautonomous systems: The case of FitzHugh–Nagumo’s model

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