Non-autonomous bifurcation in impulsive systems

M. U. Akhmet, A. Kashkynbayev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This is the first paper which considers non-autonomous bifurcations in impulsive differential equations. Impulsive generalizations of the non-autonomous pitchfork and transcritical bifurcation are discussed. We consider scalar differential equation with fixed moments of impulses. It is illustrated by means of certain systems how the idea of pullback attracting sets remains a fruitful concept in the impulsive systems. Basics of the theory are provided.

Keywords

  • Attractive solution
  • Impulsive differential equations
  • Non-autonomous bifurcation theory
  • Pitchfork bifurcation
  • Repulsive solution
  • Transcritical bifurcation

ASJC Scopus subject areas

  • Applied Mathematics

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