Work

Limit Cycles of Continuous–Discontinuous Piecewise Linear Hamiltonian Systems in ℝ 2 Separated by the Curve y =sin x

Year: 2025

Type: article

Abstract: ABSTRACT These last decades piecewise differential systems have been studied intensively, mainly due to their applications. Inside the study of the dynamics of these differential systems, the limit cycles, that is, the isolated periodic orbits inside the set of all periodic orbits of the system, play a main role. We consider continuous–discontinuous piecewise differential systems in the plane separated by the analytic curve and formed by two arbitrary linear Hamiltonian systems: continuous in the sense that the first component of the two Hamiltonian systems coincide on the curve and discontinuous in the sense that the second component of the two Hamiltonian systems are distinct on the curve . We prove that such piecewise differential systems can have four limit cycles.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70230

Authors: N. Chachapoyas, Jaume Llibre, I. S. Meza‐Sarmiento, J. Vidarte

Institutions: Universidade Federal de Itajubá, Universitat Autònoma de Barcelona

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Agencia Estatal de Investigación