Piecewise-linearized methods for oscillators with limit cycles

DOI10.1016/j.chaos.2005.04.084zbMath1108.34030OpenAlexW2120868700MaRDI QIDQ813706

Juan I. Ramos

Publication date: 13 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.04.084

zbMATH Keywords

nonlinear oscillatorslimit cyclespiecewise linearization method

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Discontinuous ordinary differential equations (34A36) Dynamical systems involving maps of the interval (37E05)

Related Items (13)

Existence of self-oscillation for a class of nonlinear discrete-time systems ⋮ Piecewise homotopy methods for nonlinear ordinary differential equations ⋮ Limit cycles of non-smooth oscillators ⋮ Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems ⋮ Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity ⋮ Piecewise-linearized methods for initial-value problems with oscillating solutions ⋮ Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic ⋮ Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic ⋮ One-step recursive method for solving systems of differential equations ⋮ The existence of the exponentially stable limit cycle for a class of nonlinear systems ⋮ Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods ⋮ Limit cycles design for a class of bilinear control systems ⋮ SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linearized perturbation technique and its applications to strongly nonlinear oscillators.
• Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers.
• The limit cycles of Liénard equations in the strongly nonlinear regime
• On limit cycle approximations in the van der Pol oscillator
• Iteration procedure for determining approximate solutions to non-linear oscillator equations
• A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations
• Analysis of the simple harmonic oscillator with fractional damping
• Preliminary analytical and numerical investigations of a van der Pol type oscillator having discontinuous dependence on the velocity
• An analysis of a nonlinear elastic force van der Pol oscillator equation
• Accurate higher-order approximations to frequencies of nonlinear oscillators with fractional powers
• MATHEMATICAL AND NUMERICAL STUDY OF THE DUFFING-HARMONIC OSCILLATOR
• OSCILLATIONS IN AN x4/3POTENTIAL
• FRACTIONAL VAN DER POL EQUATIONS
• NUMERICAL STUDY OF A NON-STANDARD FINITE-DIFFERENCE SCHEME FOR THE VAN DER POL EQUATION
• Generalization of the method of slowly varying amplitude and phase to non-linear oscillatory systems with two degrees of freedom
• Perturbation methods and non-linear hyperbolic waves
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator

This page was built for publication: Piecewise-linearized methods for oscillators with limit cycles