Yang, Jihua Picard-Fuchs equation applied to quadratic isochronous systems with two switching lines. (English) Zbl 1445.34041 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 3, Article ID 2050042, 17 p. (2020). Summary: The present paper is devoted to study the problem of limit cycle bifurcations for nonsmooth integrable differential systems with two perpendicular switching lines. By using the Picard-Fuchs equation, we obtain the upper bounds of the number of limit cycles bifurcating from the period annuli of the quadratic isochronous systems \[( S_1):\dot{x}=-y+ x^2- y^2,\;\dot{y}=x+2xy\] and \[(S_2):\dot{x}=-y+ x^2,\;\dot{y}=x+xy,\] when they are perturbed inside a class of all discontinuous polynomial differential systems of degree \(n\). This method can be applied to study the limit cycle bifurcations of other integrable differential systems. Cited in 5 Documents MSC: 34A36 Discontinuous ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 34E10 Perturbations, asymptotics of solutions to ordinary differential equations Keywords:isochronous system; limit cycle; Melnikov function; Picard-Fuchs equation PDFBibTeX XMLCite \textit{J. Yang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 3, Article ID 2050042, 17 p. (2020; Zbl 1445.34041) Full Text: DOI References: [1] Bernardo, M., Budd, C., Champneys, A. & Kowalczyk, P. [2008] Piecewise-Smooth Dynamical Systems, Theory and Applications (Springer-Verlag, London). · Zbl 1146.37003 [2] Buica, A. & Llibre, J. 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