On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

DOI10.1006/jdeq.2000.3916zbMath0984.34029OpenAlexW1966315804MaRDI QIDQ5946973

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Publication date: 14 May 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3916

zbMATH Keywords

stabilityexistenceuniquenessHopf bifurcationautonomous control systemsbounded nonlinear feedbackhysteresis nonlinearitieslarge-amplitude periodic cyclesmonotone concave and convex operatorsnonlinearities of Landesman-Lazer type

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcation theory of functional-differential equations (34K18) Hysteresis for ordinary differential equations (34C55)

Related Items (9)

A novel route to a Hopf bifurcation scenario in switched systems with dead-zone ⋮ Hopf bifurcation in symmetric networks of coupled oscillators with hysteresis ⋮ Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems ⋮ Bifurcations from a center at infinity in 3D piecewise linear systems with two zones ⋮ Pattern formation in parabolic equations containing hysteresis with diffusive thresholds ⋮ Hopf bifurcation at infinity in 3D symmetric piecewise linear systems. Application to a Bonhoeffer-van der Pol oscillator ⋮ Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems ⋮ Generalized Hopf bifurcation in a class of planar switched systems ⋮ Hopf bifurcation at infinity in 3D relay systems

Cites Work

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• Critical point theory and Hamiltonian systems
• Ranges of nonlinear asymptotically linear operators
• Conditions of cycle stability for the Hopf bifurcation at infinity
• Differential models of hysteresis
• Localization and construction of cycles in Hopf's bifurcation at infinity
• Stability of large cycles in a nonsmooth problem with Hopf bifurcation at infinity
• Asymptotics of nonlinearities and operator equations
• Hysteresis and phase transitions
• The method of parameter functionalization in the hopf bifurcation problem
• Nonlinear resonance in systems with hysteresis

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