Stability of large cycles in a nonsmooth problem with Hopf bifurcation at infinity

DOI10.1016/S0362-546X(99)00162-5zbMath0963.34034MaRDI QIDQ1585010

R. Smith

Publication date: 6 November 2000

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

stabilityexistenceHopf bifurcationlarge cyclesmonotone concave operatorsnonsmooth nonlinearities

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (9)

Hopf bifurcation in symmetric networks of coupled oscillators with hysteresis ⋮ Principal asymptotics in the problem on the Andronov-Hopf bifurcation and their applications ⋮ Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems ⋮ Hopf bifurcation at infinity and dissipative vector fields of the plane ⋮ Pattern formation in parabolic equations containing hysteresis with diffusive thresholds ⋮ Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input ⋮ On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity ⋮ Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems ⋮ Generalized Hopf bifurcation in a class of planar switched systems

Cites Work

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• 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
• Conditions of cycle stability for the Hopf bifurcation at infinity
• Localization and construction of cycles in Hopf's bifurcation at infinity
• Hopf bifurcations at infinity
• The method of parameter functionalization in the hopf bifurcation problem
• Hopf bifurcation at infinity with discontinuous nonlinearities

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