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Homoclinic and heteroclinic motions in hybrid systems with impacts

  • Mehmet Onur Fen EMAIL logo and Fatma Tokmak Fen
Published/Copyright: September 22, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 5

Abstract

In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts.

MSC 2010: Primary 34C37; Secondary 34A37
Keywords: impulsive systems; stable and unstable sets; homoclinic motion; heteroclinic motion; Duffing equation with impacts

This work is supported by the 2219 scholarship programme of TÜBİTAK, the Scientific and Technological Research Council of Turkey.

(Communicated by Michal Fečkan)

Acknowledgement

The authors wish to express their sincere gratitude to the referees for the helpful criticism and valuable suggestions, which helped to improve the paper significantly.

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Received: 2015-5-23
Accepted: 2015-12-8
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0041
Keywords for this article
impulsive systems; stable and unstable sets; homoclinic motion; heteroclinic motion; Duffing equation with impacts

Articles in the same Issue

  2. Cyclic and rotational latin hybrid triple systems
  4. Notes on mildly distributive semilattices
  6. On generalized completely distributive posets
  8. Properties of non-associative MV-algebras
  10. On the upper and lower exponential density functions
  12. Quadratic permutations, complete mappings and mutually orthogonal latin squares
  14. On F-groups with the central factor of order p4
  16. Comparison of some families of real functions in porosity terms
  18. Negative interest rates: why and how?
  20. Homoclinic and heteroclinic motions in hybrid systems with impacts
  22. Some fixed point theorems in Branciari metric spaces
  24. S-essential spectra and measure of noncompactness
  26. Unified approach to graphs and metric spaces
  28. On structural properties of porouscontinuous functions
  30. A class of topological spaces between the classes of regular and urysohn spaces
  32. On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
  34. Generalized Baskakov type operators
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