منابع مشابه
Canard cycles in Global Dynamics
Fast-slow systems are studied usually by “geometrical dissection” [4]. The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics which is seen as a parameter of the fast dynamics. A generic solution comes close to a connected component of the stable invariant sets of the fast dynamics. As the slow dynamics evolves, this attractor may lose its stability an...
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We demonstrate experimentally and theoretically the existence of canard orbits and excitable quasiharmonic limit cycles in the thermo-optical dynamics of semiconductor optical amplifiers. We also observe the phase locking of the noise-induced spikes to the small-amplitude Hopf quasiharmonic oscillations, recently predicted by Makarov, Nekorkin, and Velarde [Phys. Rev. Lett. 86, 3431 (2001)]].
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We investigate the mechanism of abrupt transition between small and large amplitude oscillationsin fast-slow piecewise-linear (PWL) models of FitzHugh-Nagumo (FHN) type. In the context ofneuroscience, these oscillatory regimes correspond to subthreshold oscillations and action potentials(spikes) respectively. The minimal model that shows such phenomenon has a cubic-like nullclin...
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The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contain...
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This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. “Canard solutions” are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a “turning point” and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the ...
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ژورنال
عنوان ژورنال: Journal of Dynamical and Control Systems
سال: 2021
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-021-09553-2