×
Liu, Xia; Han, Maoan

Hopf bifurcation for nonsmooth Liénard systems. (English) Zbl 1176.34047

Int. J. Bifurcation Chaos Appl. Sci. Eng. 19, No. 7, 2401-2415 (2009).
Summary: The Hopf cyclicity of nonsmooth Liénard systems on the plane is studied and an algebraic method to find the Hopf cyclicity is presented. A sufficient and necessary condition which ensures the origin being a center is obtained. Some new and interesting applications are presented.

Cited in 20 Documents

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C14 Symmetries, invariants of ordinary differential equations

Keywords:

Hopf cyclicity; nonsmooth; limit cycle; liapunov constant
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1006/jdeq.1996.0177 · Zbl 0901.34034 · doi:10.1006/jdeq.1996.0177
[2] DOI: 10.1142/S0218127499001231 · Zbl 1089.34512 · doi:10.1142/S0218127499001231
[3] Coll B., Discr. Contin. Dyn. Syst. 6 pp 609–
[4] DOI: 10.1006/jmaa.2000.7188 · Zbl 0973.34033 · doi:10.1006/jmaa.2000.7188
[5] DOI: 10.1007/978-94-015-7793-9 · doi:10.1007/978-94-015-7793-9
[6] DOI: 10.1142/S0218127403007618 · Zbl 1077.34031 · doi:10.1142/S0218127403007618
[7] Han M., Ann. Diff. Eqs. 15 pp 113–
[8] DOI: 10.1006/jmaa.2000.6758 · Zbl 1054.34052 · doi:10.1006/jmaa.2000.6758
[9] DOI: 10.1007/BFb0103843 · doi:10.1007/BFb0103843
[10] DOI: 10.1098/rsta.2001.0905 · Zbl 1097.37502 · doi:10.1098/rsta.2001.0905
[11] DOI: 10.1023/A:1008384928636 · Zbl 0980.70018 · doi:10.1023/A:1008384928636
[12] DOI: 10.1016/j.physd.2006.08.021 · Zbl 1111.34034 · doi:10.1016/j.physd.2006.08.021
[13] DOI: 10.1016/j.euromechsol.2006.04.004 · Zbl 1187.70041 · doi:10.1016/j.euromechsol.2006.04.004
[14] DOI: 10.1007/s00332-005-0606-8 · Zbl 1104.37031 · doi:10.1007/s00332-005-0606-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.