Global first harmonic bifurcation diagram for odd piecewise linear control systems

DOI10.1080/02681119608806216zbMath0855.93037OpenAlexW1972709249MaRDI QIDQ4883614

Jaume Llibre, Enrique Ponce

Publication date: 4 February 1997

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119608806216

zbMATH Keywords

periodic orbitsdescribing function methodfirst harmonic bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (15)

Periodic Orbit Bifurcations in Planar Hysteretic Systems without Equilibria ⋮ Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differential systems ⋮ Limit cycles of continuous and discontinuous piecewise-linear differential systems in \(\mathbb{R}^3\) ⋮ On the determination of the limit cycles using the harmonic balance method ⋮ First Harmonic Analysis of Linear Control Systems with High-Gain Saturating Feedback ⋮ Symmetry Breaking of Periodic Orbits in Control Systems: A Harmonic Balance Approach ⋮ Existence of periodic orbits of stable saturated systems ⋮ BIFURCATION ANALYSIS OF TIME-DELAY CONTROL SYSTEMS WITH SATURATION ⋮ Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+ 2)–dimension ⋮ CHARACTERIZATION OF STATIC BIFURCATIONS IN THE FREQUENCY DOMAIN ⋮ BIFURCATION OF LIMIT CYCLES FROM A FOUR-DIMENSIONAL CENTER IN CONTROL SYSTEMS ⋮ ON PERIODIC ORBITS OF 3D SYMMETRIC PIECEWISE LINEAR SYSTEMS WITH REAL TRIPLE EIGENVALUES ⋮ CHARACTERIZATION OF DYNAMIC BIFURCATIONS IN THE FREQUENCY DOMAIN ⋮ Analysis of static and dynamic bifurcations from a feedback systems perspective ⋮ Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields

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• Possible new strange attractors with spiral structure
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• Planar linear systems with single saturated feedback
• Hopf bifurcations at infinity
• The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
• Some unsolved problems in the theory of automatic control and fuzzy proofs
• Harmonic balance and the Hopf bifurcation

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