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• W3026804558 abstract "Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for oscillators which have a small-magnitude negative nontrivial Floquet exponent. This necessitates the use of the augmented phase reduction, a recently devised two-dimensional reduction technique based on isochrons and isostables. In this article, we calculate analytical expressions for the augmented phase reduction for two dynamically different planar systems: periodic orbits born out of a homoclinic bifurcation, and relaxation oscillators. To validate our calculations, we simulate models in these dynamic regimes, and compare their numerically computed augmented phase reduction with the derived analytical expressions. These analytical and numerical calculations help us to understand conditions for which the use of augmented phase reduction over the standard phase reduction can be advantageous." @default.
• W3026804558 created "2020-05-29" @default.
• W3026804558 creator A5077998932 @default.
• W3026804558 creator A5081623523 @default.
• W3026804558 date "2020-05-24" @default.
• W3026804558 modified "2023-09-26" @default.
• W3026804558 title "Augmented Phase Reduction for Periodic Orbits Near a Homoclinic Bifurcation and for Relaxation Oscillators" @default.
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• W3026804558 hasPublicationYear "2020" @default.
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