منابع مشابه
Numerical Computation of Canards
Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuat...
متن کاملFeedback control of canards.
We present a control mechanism for tuning a fast-slow dynamical system undergoing a supercritical Hopf bifurcation to be in the canard regime, the tiny parameter window between small and large periodic behavior. Our control strategy uses continuous feedback control via a slow control variable to cause the system to drift on average toward canard orbits. We apply this to tune the FitzHugh-Nagumo...
متن کاملCanards from Chua's Circuit
At first, the aim of this work is to extend Benôıt’s theorem for the generic existence of “canards” solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua’s cubic model of dimension three and four enables to state e...
متن کاملFrom Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation
In this article, we study canard solutions of the forced van der Pol equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observation made herein is that there are two branches of canards in parameter space which extend across all positive forcing frequencies. In the lowfrequency forcing regime, we demonstrate the existence of primar...
متن کاملCanards in a Surface Oxidation Reaction
Canards are periodic orbits for which the trajectory follows both the attracting and repelling parts of a slow manifold. They are associated with a dramatic change in the amplitude and period of a periodic orbit within a very narrow interval of a control parameter. It is shown numerically that canards occur in an appropriate parameter range in twoand three-dimensional models of the platinum-cat...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2001
ISSN: 0022-0396
DOI: 10.1006/jdeq.2001.4001