Slow Manifold Structure and the Emergence of Mixed-Mode Oscillations

Andrei Goryachev; Peter Strizhak; Raymond Kapral

doi:10.1063/1.474647

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Slow Manifold Structure and the Emergence of Mixed-Mode Oscillations

Andrei Goryachev·Peter Strizhak·Raymond Kapral

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Abstract

A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase locking on a 2-torus is constructed. We show that mixed-modes correspond to the periodic orbits embedded in the horseshoe-type strange set and demonstrate how transformations of this set determine the transitions of mixed-mode states into each other.

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Andrei Goryachev, Peter Strizhak, Raymond Kapral. 1997-06-26. Slow Manifold Structure and the Emergence of Mixed-Mode Oscillations. https://doi.org/10.1063/1.474647

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