Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps

V. Avrutin, Albert Granados, M. Schanz

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs.
Original languageEnglish
JournalNonlinearity
Volume24
Issue number9
Pages (from-to)2575-2598
ISSN0951-7715
DOIs
Publication statusPublished - 2011
Externally publishedYes

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