Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics

[1] A. Andronov, A. Vitt and S. Khaikin, Theory of Oscillations, Pergamon Press, Oxford, 1966. Search in Google Scholar

[2] J.C. Artés, J. Llibre, J.C. Medrado and M.A. Teixeira, Piecewise linear differential systems with two real saddles, Math. Comput. Simul. 95 (2013), 13–22.10.1016/j.matcom.2013.02.007 Search in Google Scholar

[3] R. Benterki and J. Llibre, The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves I, to appear in Dynamics of Continuous, Discrete and Impulsive Systems-Series A, 2020.10.1007/s12591-021-00564-w Search in Google Scholar

[4] R. Benterki and J. Llibre, The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves II, accepted to be published, 2020.10.1007/s12591-021-00564-w Search in Google Scholar

[5] R.Benterki and J.LLibre, Crossing Limit Cycles of Planar Piecewise Linear Hamiltonian Systems without Equilibrium Points. Mathematics 2020, 8, 755.10.3390/math8050755 Search in Google Scholar

[6] M. di Bernardo, C.J. Budd, A.R. Champneys and P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications, Appl. Math. Sci., vol. 163, Springer-Verlag, London, 2008. Search in Google Scholar

[7] R. Bix, Conics and cubics, Undergraduat Texts in Mathematics, Second Edition, Springer, 2006. Search in Google Scholar

[8] D.C. Braga and L.F.Mello, Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane, Nonlinear Dynam. 73 (2013) 128–1288. Search in Google Scholar

[9] R.D. Euzébio and J. Llibre, On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line, J. Math. Anal. Appl. 424(1) (2015), 475–486.10.1016/j.jmaa.2014.10.077 Search in Google Scholar

[10] A.F. Fonseca, J. Llibre and L.F. Mello, Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points, to appear in Int. J. Bifurcation and Chaos, 2020.10.1142/S0218127420501576 Search in Google Scholar

[11] E. Freire, E. Ponce, F. Rodrigo and F. Torres, Bifurcation sets of continuous piecewise linear systems with two zones, Int. J. Bifurcation and Chaos 8 (1998), 2073–2097.10.1142/S0218127498001728 Search in Google Scholar

[12] E. Freire, E. Ponce and F. Torres, Canonical discontinuous planar piecewise linear systems, SIAM J. Appl. Dyn. Syst. 11(1)(2012), 181–211.10.1137/11083928X Search in Google Scholar

[13] J.J. Jimenez, J. Llibre and J.C. Medrado, Crossing limit cycles for a class of piecewise linear differential centers separated by a conic, Preprint, 2019.10.14232/ejqtde.2020.1.19 Search in Google Scholar

[14] J. Llibre, D.D. Novaes and M.A. Teixeira, Limit cycles bifurcating from the periodic orbits of a discontinuous piecewise linear differential center with two zones, Int. J. Bifurcation and Chaos 25 (2015), 1550144, pp. 11. Search in Google Scholar

[15] J. Llibre and E. Ponce, Piecewise linear feedback systems with arbitrary number of limit cycles, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), 895–904.10.1142/S0218127403007047 Search in Google Scholar

[16] J. Llibre, E. Ponce and X. Zhang, Existence of piecewise linear differential systems with exactly n limit cycles for all n ∈ 𝕅, Nonlinear Anal. 54 (2003) 977–994.10.1016/S0362-546X(03)00122-6 Search in Google Scholar

[17] J. Llibre and E. Ponce, Three nested limit cycles in discontinuous piecewise linear differential systems with two zones, Dyn. Contin. Discr. Impul. Syst., Ser. B 19 (2012), 325–335. Search in Google Scholar

[18] J. Llibre and M.A. Teixeira, Piecewise linear differential systems with only centers can create limit cycles ?, Nonlinear Dyn. 91 (2018), 249–255.10.1007/s11071-017-3866-6 Search in Google Scholar

[19] J. Llibre and X. Zhang, Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve, Int. J. Bifurcation and Chaos 29 (2019), 1950017, pp. 17. Search in Google Scholar

[20] O. Makarenkov and J.S.W. Lamb, Dynamics and bifurcations of nonsmooth systems: a survey, Phys. D 241 (2012), 1826–1844.10.1016/j.physd.2012.08.002 Search in Google Scholar

[21] D.J.W. Simpson, Bifurcations in Piecewise-Smooth Continuous Systems, World Sci. Ser. Nonlinear Sci. Ser. A, vol. 69, World Scientific, Singapore, 2010.10.1142/7612 Search in Google Scholar