BIFURCATION OF LIMIT CYCLES FROM A FOUR-DIMENSIONAL CENTER IN CONTROL SYSTEMS

DOI10.1142/S0218127405013599zbMath1092.34519OpenAlexW1972123340MaRDI QIDQ5474315

Adriana Buică, Jaume Llibre

Publication date: 23 June 2006

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

Full work available at URL: https://doi.org/10.1142/s0218127405013599

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamical systems in control (37N35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (11)

Stability of periodic solutions for Lipschitz systems obtained via the averaging method ⋮ Limit cycles for a mechanical system coming from the perturbation of a four-dimensional linear center ⋮ Bifurcation of limit cycles from a two-dimensional center inside ⋮ Limit cycles for two classes of control piecewise linear differential systems ⋮ HYPERBOLIC PERIODIC ORBITS FROM THE BIFURCATION OF A FOUR-DIMENSIONAL NONLINEAR CENTER ⋮ On the limit cycles of a class of piecewise linear differential systems in \(\mathbb R^4\) with two zones ⋮ Bifurcation of limit cycles of a class of piecewise linear differential systems in \(\mathfrak R^4\) with three zones ⋮ Bifurcation of limit cycles from an \(n\)-dimensional linear center inside a class of piecewise linear differential systems ⋮ ON THREE-PARAMETER FAMILIES OF FILIPPOV SYSTEMS — THE FOLD–SADDLE SINGULARITY ⋮ Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention \(2n\) ⋮ Bifurcation of limit cycles from a 4-dimensional center in \(1:n\) resonance

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Existence of piecewise linear differential systems with exactly \(n\) limit cycles for all \(n\in \mathbb N\)
• Averaging methods for finding periodic orbits via Brouwer degree.
• Bifurcations of periodic orbits, subharmonic solutions and invariant Tori of high-dimensional systems
• PIECEWISE LINEAR FEEDBACK SYSTEMS WITH ARBITRARY NUMBER OF LIMIT CYCLES
• Global first harmonic bifurcation diagram for odd piecewise linear control systems
• Phase portraits of planar control systems
• On simplifying and classifying piecewise-linear systems
• LIMIT CYCLE BIFURCATION FROM CENTER IN SYMMETRIC PIECEWISE-LINEAR SYSTEMS

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