Analysis of Degenerate Fold–Hopf Bifurcation in a Three-Dimensional Differential System

Tigan, Gheorghe

doi:10.1007/s12346-017-0241-4

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…We find that the normal form coefficient G 011 (0) ¼ 0 across a range of parameter values, indicating the ZH bifurcation is degenerate. The normal form equations for degenerate ZH bifurcations are not well known and previous studies have focused on different cases [73,74]. Tigan et al [75] showed that a degenerate ZH bifurcation with G 011 (0) ¼ 0 occurs in a Rö ssler-type system and used averaging theory to detect periodic orbits, leaving the structure of global bifurcations unresolved.…”

Section: Appendix a Further Study Of Degenerate Bogdanov -Takens And Zero-hopf Bifurcationsmentioning

confidence: 99%

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis

et al. 2019

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We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov–Takens and zero-Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner.

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Section: Appendix a Further Study Of Degenerate Bogdanov -Takens And Zero-hopf Bifurcationsmentioning

confidence: 99%

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis

et al. 2019

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“…Hence, if n ∈ I the system (15) undergoes fold-Hopf bifurcations, degenerate or not. We started to study a form of the system (15) in [19] where we obtained insights on the existence of periodic orbits. We used an approach based on averaging theory.…”

Section: Example 1 Consider the 3d Differential Systeṁmentioning

confidence: 99%

Degenerate with respect to parameters fold-Hopf bifurcations

Tigan¹

2017

Discrete &Amp; Continuous Dynamical Systems - A

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In this work we study degenerate with respect to parameters fold-Hopf bifurcations in three-dimensional differential systems. Such degeneracies arise when the transformations between parameters leading to a normal form are not regular at some points in the parametric space. We obtain new generic results for the dynamics of the systems in such a degenerate framework. The bifurcation diagrams we obtained show that in a degenerate context the dynamics may be completely different than in a non-degenerate framework.

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Four-dimensional Zero-Hopf Bifurcation of Quadratic Polynomial Differential System, via Averaging Theory of Third Order

2021

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Analysis of Degenerate Fold–Hopf Bifurcation in a Three-Dimensional Differential System

Cited by 4 publications

References 14 publications

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis

Degenerate with respect to parameters fold-Hopf bifurcations

Four-dimensional Zero-Hopf Bifurcation of Quadratic Polynomial Differential System, via Averaging Theory of Third Order

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