Limit Cycles of Continuous Piecewise Smooth Differential Systems

Author(s)

Casimiro, Joyce A. ; Llibre, Jaume

• Document type: Journal article
• Source: Results in Mathematics; v. 78, n. 5, p. 14-pg., 2023-10-01.

Abstract

From the beginning of this century many articles have been published on the continuous and discontinuous piecewise differential systems specially in the plane. The big interest on these piecewise differential systems mainly comes from their increasing number of applications for modelling many natural phenomena. As it is usual in the planar differential systems one of the main difficulties for understanding their dynamics consists in controlling their limit cycles. The major part of papers studying continuous piecewise differential systems has an straight line as the line of separation between the differential systems forming the continuous piecewise differential systems. In this work we consider continuous piecewise differential systems separated by a circle and formed by one linear differential center and one quadratic differential center. We study the maximum number of limit cycles that such kind of continuos piecewise differential system can exhibit. (AU)

• FAPESP's process: 22/01375-7 - Limit cycles of discontinuous piecewise smooth differential systems in the plane R2 and in the space R3
• Grantee: Joyce Aparecida Casimiro
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 18/25575-0 - Piecewise smooth differential equations in dimension 3
• Grantee: Joyce Aparecida Casimiro
• Support Opportunities: Scholarships in Brazil - Doctorate