Existence of piecewise linear differential systems with exactly \(n\) limit cycles for all \(n\in \mathbb N\)

DOI10.1016/S0362-546X(03)00122-6zbMath1039.34023MaRDI QIDQ1400272

Enrique Ponce, Xiang Zhang, Jaume Llibre

Publication date: 13 August 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

limit cyclesnonlinear oscillationspiecewise linear control systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (16)

Bifurcation of limit cycles for a perturbed piecewise quadratic differential systems ⋮ Center boundaries for planar piecewise-smooth differential equations with two zones ⋮ Piecewise linear differential system with a center-saddle type singularity ⋮ The 16th Hilbert problem for discontinuous piecewise linear differential systems separated by the algebraic curve \(y = x^n\) ⋮ The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems ⋮ On piecewise linear differential systems with \(n\) limit cycles of arbitrary multiplicities in two zones ⋮ Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear Systems ⋮ Existence of Homoclinic Cycles and Periodic Orbits in a Class of Three-Dimensional Piecewise Affine Systems ⋮ Phase portraits of continuous piecewise linear Liénard differential systems with three zones ⋮ Unnamed Item ⋮ ON THE NUMBER OF LIMIT CYCLES IN PIECEWISE-LINEAR LIÉNARD SYSTEMS ⋮ The matching of two stable sewing linear systems in the plane ⋮ Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones ⋮ BIFURCATION OF LIMIT CYCLES FROM A FOUR-DIMENSIONAL CENTER IN CONTROL SYSTEMS ⋮ The Number of Limit Cycles Bifurcating from a Degenerate Center of Piecewise Smooth Differential Systems ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Cites Work

• Qualitative investigation of a piecewise linear system
• Branching phenomena for periodic solutions of non-autonomous piecewise linear systems
• Investigation of a piecewise linear dynamical system with three parameters
• Heteroclinic bifurcations in damped rigid block motion
• PIECEWISE LINEAR FEEDBACK SYSTEMS WITH ARBITRARY NUMBER OF LIMIT CYCLES
• LIMIT CYCLE BIFURCATION FROM CENTER IN SYMMETRIC PIECEWISE-LINEAR SYSTEMS
• Forced Oscillations and Convex Superposition in Piecewise-Linear Systems
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