Global secondary bifurcation, symmetry breaking and period-doubling
Rainer Mandel
TL;DR
This paper establishes a criterion for global secondary bifurcation through symmetry breaking and demonstrates period-doubling bifurcations in the Lugiato-Lefever equation.
Contribution
It introduces a new criterion for global secondary bifurcation via symmetry breaking and applies it to prove period-doubling bifurcations in a specific nonlinear equation.
Findings
Criterion for global secondary bifurcation via symmetry breaking
Proof of period-doubling bifurcations in the Lugiato-Lefever equation
Advancement in understanding bifurcation phenomena
Abstract
In this paper we provide a criterion for global secondary bifurcation via symmetry breaking. As an application, the occurrence of period-doubling bifurcations for the Lugiato-Lefever equation is proved.
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