Transcritical and zero-Hopf bifurcations in the Genesio system
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DOI: 10.1007/s11071-016-3259-2
Abstract: In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation $${\dddot{x}} + a {\ddot{x}} + b {\dot{x}} + c x - x^2 = 0$$x⃛+ax¨+bx˙+cx-x2=0, called the Genesio… read more here.
Keywords: bifurcations genesio; system; hopf bifurcations; zero hopf ... See more keywords
An analytical method for studying double Hopf bifurcations induced by two delays in nonlinear differential systems
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DOI: 10.1007/s11431-019-9673-6
Abstract: An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively. As an illustrative example, the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in… read more here.
Keywords: analytical method; hopf bifurcations; double hopf; two delays ... See more keywords
Hopf bifurcations in quaternary dynamical systems of rotating thermofluid mixtures, driven by spectrum characteristic coefficients
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DOI: 10.1007/s11587-020-00514-8
Abstract: The paper is concerned with the onset of bifurcations in fluid mixtures. The instability of thermal conduction state in a rotating fluid layer heated and salted from below, is analyzed. The Taylor number threshold for… read more here.
Keywords: systems rotating; hopf bifurcations; rotating thermofluid; bifurcations quaternary ... See more keywords
Lyapunov coefficients for degenerate Hopf bifurcations and an application in a model of competing populations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.05.040
Abstract: Abstract This paper focuses on the study of codimension one and two Hopf bifurcations and the pertinent Lyapunov stability coefficients for a general reaction–diffusion system. We display algebraic expressions for the first and second Lyapunov… read more here.
Keywords: lyapunov coefficients; hopf bifurcations; model; bifurcations application ... See more keywords
Efficient reduction for diagnosing Hopf bifurcation in delay differential systems: Applications to cloud-rain models.
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DOI: 10.1063/5.0004697
Abstract: By means of Galerkin-Koornwinder (GK) approximations, an efficient reduction approach to the Stuart-Landau (SL) normal form and center manifold is presented for a broad class of nonlinear systems of delay differential equations that covers the… read more here.
Keywords: hopf bifurcations; efficient reduction; hopf bifurcation; bifurcation ... See more keywords
Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures.
Sign Up to like & getrecommendations! Published in 2017 at "Physical Review E"
DOI: 10.1103/physreve.95.042410
Abstract: A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form… read more here.
Keywords: critical dynamics; transitions normal; hopf bifurcations; physiology ... See more keywords