Blue sky-like catastrophe for reversible nonlinear implicit ODEs

Flaviano  Battelli; Michal Fečkan

doi:10.3934/dcdss.2016034

Article Contents

2016, Volume 9, Issue 4: 895-922. Doi: 10.3934/dcdss.2016034

This issue Previous Article Preface Next Article Mesochronic classification of trajectories in incompressible 3D vector fields over finite times

Blue sky-like catastrophe for reversible nonlinear implicit ODEs

Flaviano Battelli^1, and
Michal Fečkan^2,

1.
Department of Industrial Engeneering and Mathematics, Marche Polytecnic University, Ancona
2.
Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava

Received: March 2015

Revised: June 2015

Published: August 2016

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Abstract

We study for reversible implicit differential equations the bifurcation of bounded solutions connecting singularities in finite time and their approximation by shadowed periodic solutions. Melnikov like condition is derived. Application is given to planar nonlinear RLC system.

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Mathematics Subject Classification: Primary: 34A09, 34C23; Secondary: 37G40.

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References

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