Lyapunov Coefficients for Degenerate Hopf Bifurcations
Jorge Sotomayor, Luis Fernando Mello, Denis de Carvalho Braga
TL;DR
This paper investigates various codimension Hopf bifurcations and computes their Lyapunov stability coefficients using computer-assisted algebraic methods.
Contribution
It provides algebraic expressions for Lyapunov coefficients across multiple codimensions of Hopf bifurcations, enhancing understanding of bifurcation stability.
Findings
Derived explicit algebraic formulas for Lyapunov coefficients
Analyzed codimension one to four Hopf bifurcations
Utilized computer-assisted calculations for complex algebraic expressions
Abstract
In this paper are studied the codimensions one, two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients. Algebraic expressions obtained with computer assisted calculations are displayed.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematical and Theoretical Epidemiology and Ecology Models · Quantum chaos and dynamical systems