On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
Tài liệu tham khảo
Yan-Qian, 1986, vol. 66
Zhifen, 1992, vol. 101
Hilbert, 1900, Mathematische Probleme, Lecture, Second Internat. Congr. Math. (Paris, 1900), Nachr. Ges. Wiss. Göttingen Math. Phys. Kl., 253
Smale, 1998, Mathematical problems for the next century, Math. Intelligencer, 20, 7, 10.1007/BF03025291
Carletti, 2005, A note on existence and uniqueness of limit cycles for Liénard systems, J. Math. Anal. Appl., 307, 763, 10.1016/j.jmaa.2005.01.054
Dumortier, 1996, On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations, Nonlinearity, 9, 1489, 10.1088/0951-7715/9/6/006
Dumortier, 1990, Cubic Liénard equations with linear damping, Nonlinearity, 3, 1015, 10.1088/0951-7715/3/4/004
Khibnik, 1998, Global study of a family of cubic Liénard equations, Nonlinearity, 11, 1505, 10.1088/0951-7715/11/6/005
Xiao, 2003, On the uniqueness and nonexistence of limit cycles for predator–prey systems, Nonlinearity, 16, 1185, 10.1088/0951-7715/16/3/321
Llibre, 1996, Phase portraits of planar control systems, Nonlinear Anal., 27, 117, 10.1016/0362-546X(95)00129-J
Freire, 1998, Bifurcation sets of continuous piecewise linear systems with two zones, Internat. J. Bifur. Chaos, 8, 2073, 10.1142/S0218127498001728
Hogan, 2003, Relaxation oscillations in a system with a piecewise smooth drag coefficient, J. Sound Vib., 263, 467, 10.1016/S0022-460X(02)01431-1
van Horssen, 2005, On oscillations in a system with a piecewise smooth coefficient, J. Sound Vib., 283, 1229, 10.1016/j.jsv.2004.07.012
Giannakopoulos, 2001, Planar systems of piecewise linear differential equations with a line of discontinuity, Nonlinearity, 14, 1611, 10.1088/0951-7715/14/6/311
Zou, 2006, Generalized Hopf bifurcations for planar Filippov systems continuous at the origin, J. Nonlinear Sci., 16, 159, 10.1007/s00332-005-0606-8
Carmona, 2002, On simplifying and classifying piecewise linear systems, IEEE Trans. Circuits Syst. I, 49, 609, 10.1109/TCSI.2002.1001950
Dumortier, 2006
Freire, 2002, Bifurcation sets of continuous piecewise linear systems with three zones, Internat. J. Bifur. Chaos, 12, 1675, 10.1142/S0218127402005509
Llibre, 2002, Limit cycles for planar piecewise linear differential systems via first integrals, Qual. Theory Dyn. Syst., 3, 29, 10.1007/BF02969332
Coombes, 2008, Neuronal networks with gap junctions: a study of piecewise linear planar neuron models, SIAM J. Appl. Dyn. Syst., 7, 1101, 10.1137/070707579
Freire, 1997, Transformaciones de Filippov en sistemas lineales a trozos, Actas V Congr. Mat. Apl. Ser. Publ. Univ. Vigo I, 273
Flatto, 1964, Limit cycle studies for circuits containing one Esaki diode, J. Math. Anal. Appl., 9, 360, 10.1016/0022-247X(64)90023-X
Bautin, 1974, Qualitative investigation of a piecewise-linear system, J. Appl. Math. Mech., 38, 691, 10.1016/0021-8928(74)90020-3
Bragin, 2011, Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits, J. Comput. Syst. Sci. Int., 50, 511, 10.1134/S106423071104006X
Leonov, 2009, 89
Massera, 1954, Sur un théorème de G. Sansone sur l’equation de Liénard, Boll. Unione Mat. Ital., 9, 367
Sabatini, 2010, On the uniqueness of limit cycles for Liénard equations: the legacy of G. Sansone, Matematiche (Italy), 65
Hartman, 1982
Jordan, 2007
Freire, 2012, Canonical discontinuous planar piecewise linear systems, SIAM J. Appl. Dyn. Syst., 11, 181, 10.1137/11083928X