Browse Journals

[1] H. Giacomini and S. Neukirch, Number of limit cycles of the Liénard equation, Physical Review E 56(4) (1997), 3809-3813.

DOI: https://doi.org/10.1103/PhysRevE.56.3809

[2] J. Rayleigh, The Theory of Sound, Dover, New York, 1945.

[3] B. van der Pol, On relaxation-oscillations, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11) (1926), 978-992.

DOI: https://doi.org/10.1080/14786442608564127

[4] A. Liénard, Étude des oscillations entreténues, Revue Générale de l’Électricité 23 (1928), 901-912.

[5] A. Liénard, Étude des oscillations entreténues, Revue Générale de l’Électricité 23 (1928), 946-954.

[6] N. Levinson and O. Smith, A general equation for relaxation oscillations, Duke Mathematical Journal 9(2) (1942), 382-403.

DOI: https://doi.org/10.1215/S0012-7094-42-00928-1

[7] W. A. Albarakati, N. G. Lloyd and J. M. Pearson, Transformation to Liénard form, Electronic Journal of Differential Equations 76 (2000), 1-11.

[8] S. Lynch and C. J. Christopher, Limit cycles in highly non-linear differential equations, Journal of Sound and Vibration 224(3) (1999), 505-517.

DOI: https://doi.org/10.1006/jsvi.1999.2199

[9] A. O. Ignat’ev and V. V. Kirichenko, On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation, Mathematical Notes 93(1-2) (2013), 75-82.

DOI: https://doi.org/10.1134/S0001434613010082

[10] T. T. Bowman, Periodic solutions of Liénard systems with symmetries, Nonlinear Analysis: Theory, Methods & Applications 2(4) (1978), 457-464.

DOI: https://doi.org/10.1016/0362-546X(78)90052-4

[11] T. Carletti and G. Villari, A note on existence and uniqueness of limit cycles for Liénard systems, Journal of Mathematical Analysis and Applications 307(2) (2005), 763-773.

DOI: https://doi.org/10.1016/j.jmaa.2005.01.054

[12] K. Odani, Existence of exactly N-periodic solutions for Liénard systems, Funkcialaj Ekvacioj 39 (1996), 217-234.

DOI: https://doi.org/10.11501/3098859

[13] A. F. Filippov, A sufficient condition for the existence of a stable limit cycle for an equation of the second order, Matematicheskii Sbornik: Novaya Seriya 30(1) (1952), 171-180 (in Russian).

[14] D. A. Neumann and L. Sabbagh, Periodic solutions of Liénard systems, Journal of Mathematical Analysis and Applications 62(1) (1978), 148-156.

DOI: https://doi.org/10.1016/0022-247X(78)90226-3

[15] J. Sugie and T. Hara, Non-existence of periodic solutions of the Liénard system, Journal of Mathematical Analysis and Applications 159(1) (1991), 224-236.

DOI: https://doi.org/10.1016/0022-247X(91)90232-O

[16] M. Sabatini, On the period function of Liénard systems, Journal of Differential Equation 152(2) (1999), 467-487.

DOI: https://doi.org/10.1006/jdeq.1998.3520

[17] Yuli Cao and Changjian Liu, The estimate of the amplitude of limit cycles of symmetric Liénard systems, Journal of Differential Equation 262(3) (2017), 2025-2038.

DOI: https://doi.org/10.1016/j.jde.2016.10.034

[18] Yang Lijun and Zeng Xianwu, An upper bound for the amplitude of limit cycles in Liénard systems with symmetry, Journal of Differential Equation 258(8) (2015), 2701-2710.

DOI: https://doi.org/10.1016/j.jde.2014.12.021

[19] N. G. Lloyd, Liénard systems with several limit cycles, Mathematical Proceedings of the Cambridge Philosophical Society 102(3) (1987), 565-572.

DOI: https://doi.org/10.1017/S0305004100067608

[20] N. N. Krasovskii, Stability of Motion: Applications of Lyapunov’s Second Method to Differential Systems and Equations with delay, Stanford University Press, Stanford, California, 1963.

[21] M. Sabatini and G. Villari, On the uniqueness of limit cycles for Liénard equations: The legacy of G. Sansone, Le Matematiche (Catania) 65(2) (2010), 201-214.

[22] G. Sansone, Sopra l’equazione di A. Liénard delle oscillazioni di rilassamento, Annali di Matematica Pura ed Applicata 28(4) (1949), 153-181.

DOI: https://doi.org/10.1007/BF02411124

[23] A. D. Smirnov, Lectures on models of macroeconomics, Economic Journal of Higher School of Economics 4(1) (2000), 87-122 (in Russian).

[24] J. D. Meiss, Differential Dynamical Systems, Society for Industrial and Applied Mathematics, Philadelphia, 2007.

[25] K. Odani, The limit cycle of the van der Pol equation is not algebraic, Journal of Differential Equations 115(1) (1995), 146-152.

DOI: https://doi.org/10.1006/jdeq.1995.1008

[26] A. A. Dorodnitsyn, Asymptotic solution of van der Pol equation, Journal of Applied Mathematics and Mechanics 11(3) (1947), 313-328.

[27] V. F. Sudakov, On the question of the limit cycle of the Van der Pol generator in relaxation mode, Vestnik MGTU im. Baumana. Ser. Priborostroenie 1 (2013), 51-57 (in Russian).

[28] A. Buonomo, The periodic solution of van der Pol’s equation, SIAM Journal on Applied Mathematics 59(1) (1999), 156-171.

DOI: https://doi.org/10.1137/S0036139997319797

[29] J. A. Zonneveld, Periodic solutions of the Van der Pol equation, Nederl. Akad. Wetensch. Proc. Ser. A 69=Indag. Math. 28 (1966), 620-622.

[30] D. Greenspan, Numerical approximation of periodic solutions of van der Pol’s equation, Journal of Mathematical Analysis and Applications 39(3) (1972), 574-579.

DOI: https://doi.org/10.1016/0022-247X(72)90181-3

[31] K. Odani, On the limit cycle of the Liénard equation, Archivum Mathematicum 36(1) (2000), 25-31.

[32] N. Turner, P. V. E. McClintock and A. Stefanovska, Maximum amplitude of limit cycles in Liénard systems, Physical Review E 91(1) (2015); Article 012927 (1-13).

DOI: https://doi.org/10.1103/PhysRevE.91.012927