منابع مشابه
An elementary model of torus canards.
We study the recently observed phenomena of torus canards. These are a higher-dimensional generalization of the classical canard orbits familiar from planar systems and arise in fast-slow systems of ordinary differential equations in which the fast subsystem contains a saddle-node bifurcation of limit cycles. Torus canards are trajectories that pass near the saddle-node and subsequently spend l...
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 کاملNew dynamics in cerebellar Purkinje cells: torus canards.
We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that-after a saddle node bifurcation of limit cycles-the full model dynamics temporarily follow a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical ap...
متن کاملA showcase of torus canards in neuronal bursters
Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which we show arises in a broad array of...
متن کاملNumerical 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...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2017
ISSN: 0167-2789
DOI: 10.1016/j.physd.2017.06.005