NON-AUTONOMOUS BIFURCATION IN IMPULSIVE SYSTEMS


AKHMET M. , Kashkynbayev A.

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, no.74, pp.1-23, 2013 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2013
  • Title of Journal : ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
  • Page Numbers: pp.1-23
  • Keywords: Non-autonomous bifurcation theory, impulsive differential equations, attractive solution, repulsive solution, pitchfork bifurcation, transcritical bifurcation, COCYCLE ATTRACTORS, PITCHFORK, BEHAVIOR

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.