Attractivity and Hopf bifurcation

DOI10.1016/0362-546X(79)90039-7zbMath0423.34062OpenAlexW2057061442MaRDI QIDQ5904224

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Publication date: 1979

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(79)90039-7

zbMATH Keywords

Hopf bifurcationattractivityFitzhugh equationsasymptotically stable bifurcating periodic orbitsPoincare procedureTakens singularities

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Asymptotic properties of solutions to ordinary differential equations (34D05) General theory for ordinary differential equations (34A99)

Related Items (18)

Hopf bifurcation and related stability problems for periodic differential systems ⋮ Combining stability with symmetry properties in bifurcation problems ⋮ Degenerate Hopf bifurcation in two dimensions ⋮ Attractivity and Hopf bifurcation in Banach spaces ⋮ Attractivity properties of closed orbits in a case of generalized Hopf bifurcation ⋮ Asymptotic analysis of an industrial dynamic model. ⋮ First and invariant integrals in stability problems. ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ Bifurcation of closed orbits from a limit cycle in \(R^ 2\). ⋮ Perturbed dynamical systems: Displacement and bifurcation functions ⋮ Stable oscillations in a predator-prey model with time lag ⋮ Stable oscillations in a predator-prey model with time lag ⋮ Zip bifurcation in a competition model ⋮ Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems ⋮ Generalized hopf bifurcation and h-asymptotic stability ⋮ Periodic solutions for retarded differential systems close to ordinary ones ⋮ Generalized bifurcation of higher dimensional tori ⋮ Bifurcation and total stability

Cites Work

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• A higher-order Hopf bifurcation formula and its application to Fitzhugh's nerve conduction equation
• Liapunov direct method in approaching bifurcation problems
• An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations
• The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system
• On the nature of turbulence
• Normal forms for certain singularities of vectorfields

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