Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

Erli Zhang (), Jihua Yang and Stanford Shateyi ()
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Erli Zhang: School of Statistics and Big Data, Zhengzhou College of Finance and Economics, Zhengzhou 450044, China
Jihua Yang: School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2023, vol. 11, issue 21, 1-14

Abstract: Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are dealt with. A Melnikov mapping whose order is one is implicitly obtained by finding its originators when the system is perturbed under any nth degree of real polynomials. Then, the approach employing the Picard–Fuchs mapping is utilized to attain a higher boundary of bifurcation LCNs of systems composed of PSD functions with a global center. The method we used could be implemented to examine the problems related to the LC of other PSDS.

Keywords: Melnikov function; limit cycles (LCs); Picard–Fuchs (PF) equation; piecewise smooth differential system (PSDS) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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