Global Analysis on the Discontinuous Limit Case of a Smooth Oscillator

DOI10.1142/S0218127416500619zbMath1338.34040OpenAlexW2345988157MaRDI QIDQ2814176

Hebai Chen

Publication date: 20 June 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500619

zbMATH Keywords

limit cycleFilippov systemSD oscillatorgrazing looppseudo-saddle

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) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Discontinuous ordinary differential equations (34A36)

Related Items (14)

Existence and stability of periodic oscillations of a smooth and discontinuous oscillator ⋮ Global dynamics of degenerate linear differential systems with symmetry and two parallel switching lines ⋮ The discontinuous limit case of an archetypal oscillator with a constant excitation and van der Pol damping ⋮ Global dynamics of a SD oscillator ⋮ An oscillator with two discontinuous lines and Van der Pol damping ⋮ Global dynamics for a class of tristable system with negative stiffness ⋮ Global Dynamics of a Planar Filippov System with Symmetry ⋮ Crossing periodic orbits of nonsmooth Liénard systems and applications ⋮ Periodic solutions of discontinuous damped Duffing equations ⋮ Stability and Bifurcation in a Logistic Model with Allee Effect and Feedback Control ⋮ The Poincaré bifurcation of a SD oscillator ⋮ Global Analysis on a Discontinuous Dynamical System ⋮ Limit Cycles and Bifurcations in a Class of Discontinuous Piecewise Linear Systems ⋮ Dynamical analysis of a two species amensalism model with Beddington-DeAngelis functional response and Allee effect on the second species

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Piecewise-smooth dynamical systems. Theory and applications
• Bifurcation phenomena in non-smooth dynamical systems
• Qualitative theory of planar differential systems
• Bifurcations in Nonsmooth Dynamical Systems
• One-Parameter Bifurcations in Planar Filippov Systems
• LIMIT CYCLE BIFURCATION FROM CENTER IN SYMMETRIC PIECEWISE-LINEAR SYSTEMS
• PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS
• Global Phase Portraits of Memristor Oscillators
• Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics
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