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Volumn 30, Issue 5, 2006, Pages 1048-1068

Limit cycles in generalized Liénard systems

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; FRACTALS; NUMERICAL METHODS; OPTIMIZATION; SOLITONS;

EID: 33745831895     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.09.008     Document Type: Article
Times cited : (48)

References (24)
  • 1
    • 0000832248 scopus 로고
    • Mathematical problems
    • (M. Newton, Transl.)
    • Hilbert D. Mathematical problems. (M. Newton, Transl.). Bull Amer Math 8 (1902) 437-479
    • (1902) Bull Amer Math , vol.8 , pp. 437-479
    • Hilbert, D.1
  • 2
    • 0002587254 scopus 로고    scopus 로고
    • Mathematical problems for the next century
    • Smale S. Mathematical problems for the next century. Math Intel 20 (1998) 7-15
    • (1998) Math Intel , vol.20 , pp. 7-15
    • Smale, S.1
  • 3
    • 0037246396 scopus 로고    scopus 로고
    • Hilbert's 16th problem and bifurcations of planar polynomial vector fields
    • Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Int J Bifurcat Chaos 13 (2003) 47-106
    • (2003) Int J Bifurcat Chaos , vol.13 , pp. 47-106
    • Li, J.1
  • 4
    • 0000495631 scopus 로고
    • On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
    • Bautin N.N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Mat Sbornik (N.S.) 30 72 (1952) 181-196
    • (1952) Mat Sbornik (N.S.) , vol.30 , Issue.72 , pp. 181-196
    • Bautin, N.N.1
  • 5
    • 0038241447 scopus 로고
    • Necessary and sufficient conditions for the existence of center
    • Kukles I.S. Necessary and sufficient conditions for the existence of center. Dokl Akad Nauk 42 (1944) 160-163
    • (1944) Dokl Akad Nauk , vol.42 , pp. 160-163
    • Kukles, I.S.1
  • 6
    • 0001211762 scopus 로고
    • Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
    • Li J., and Liu Z. Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system. Publ Math 35 (1991) 487-506
    • (1991) Publ Math , vol.35 , pp. 487-506
    • Li, J.1    Liu, Z.2
  • 7
    • 3042571812 scopus 로고
    • On the singularity values of complex autonomous differential systems
    • [in Chinese]
    • Liu Y., and Li J. On the singularity values of complex autonomous differential systems. Sci China (Ser A) 3 (1989) 2450-2455 [in Chinese]
    • (1989) Sci China (Ser A) , vol.3 , pp. 2450-2455
    • Liu, Y.1    Li, J.2
  • 8
    • 0009530005 scopus 로고
    • Criteria for center of a differential equation
    • Malkin K.E. Criteria for center of a differential equation. Volg Matem Sbornik 2 (1964) 87-91
    • (1964) Volg Matem Sbornik , vol.2 , pp. 87-91
    • Malkin, K.E.1
  • 9
    • 0012780336 scopus 로고    scopus 로고
    • Liapunov constants and Hopf cyclicity of Liénard systems
    • Han M. Liapunov constants and Hopf cyclicity of Liénard systems. Ann Diff Eqs 15 2 (1999) 113-126
    • (1999) Ann Diff Eqs , vol.15 , Issue.2 , pp. 113-126
    • Han, M.1
  • 11
    • 2942666280 scopus 로고    scopus 로고
    • Bifurcation of limit cycles for a cubic Hamiltonian system under quartic perturbations
    • Zhang T., Han M., Zang H., and Meng X. Bifurcation of limit cycles for a cubic Hamiltonian system under quartic perturbations. Chaos, Solitons & Fractals 22 (2004) 1127-1138
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 1127-1138
    • Zhang, T.1    Han, M.2    Zang, H.3    Meng, X.4
  • 12
    • 33745849816 scopus 로고    scopus 로고
    • Yu P. Limit cycles in 3rd-order planar system. In: International congress of mathematicians, Beijing, China, August 20-28, 2002.
  • 13
    • 33745817513 scopus 로고    scopus 로고
    • Yu P. Twelve limit cycles in a cubic case of the 16th Hilbert problem. In: Workshop on bifurcation theory and spatio-temporal pattern formation in PDE, Toronto, Canada, December 11-13, 2003.
  • 14
    • 2942646689 scopus 로고    scopus 로고
    • A study on the existence of limit cycles of a planar system with 3rd-degree polynomials
    • Han M., Lin Y., and Yu P. A study on the existence of limit cycles of a planar system with 3rd-degree polynomials. Int J Bifurcat Chaos 14 1 (2004) 41-60
    • (2004) Int J Bifurcat Chaos , vol.14 , Issue.1 , pp. 41-60
    • Han, M.1    Lin, Y.2    Yu, P.3
  • 17
    • 24144462859 scopus 로고    scopus 로고
    • Twelve limit cycles in a cubic case of the 16th Hilbert problem
    • Yu P., and Han M. Twelve limit cycles in a cubic case of the 16th Hilbert problem. Int J Bifurcat Chaos 15 7 (2005) 2191-2205
    • (2005) Int J Bifurcat Chaos , vol.15 , Issue.7 , pp. 2191-2205
    • Yu, P.1    Han, M.2
  • 18
    • 0001790023 scopus 로고    scopus 로고
    • Computation of normal forms via a perturbation technique
    • Yu P. Computation of normal forms via a perturbation technique. J Sound Vib 211 (1998) 19-38
    • (1998) J Sound Vib , vol.211 , pp. 19-38
    • Yu, P.1
  • 20
    • 0000873906 scopus 로고
    • On relaxation-oscillations
    • van der Pol B. On relaxation-oscillations. Philos Mag 7 (1926) 901-912
    • (1926) Philos Mag , vol.7 , pp. 901-912
    • van der Pol, B.1
  • 22
    • 0001375813 scopus 로고    scopus 로고
    • Limit cycles in highly non-linear differential equations
    • Lynch S., and Christopher C.J. Limit cycles in highly non-linear differential equations. J Sound Vib 224 3 (1999) 505-517
    • (1999) J Sound Vib , vol.224 , Issue.3 , pp. 505-517
    • Lynch, S.1    Christopher, C.J.2
  • 23
    • 0036183885 scopus 로고    scopus 로고
    • Symmetry in planar dynamical systems
    • Lloyd N., and Pearson J. Symmetry in planar dynamical systems. J Symbolic Comput 33 (2002) 357-366
    • (2002) J Symbolic Comput , vol.33 , pp. 357-366
    • Lloyd, N.1    Pearson, J.2
  • 24
    • 0009268934 scopus 로고    scopus 로고
    • Generalized cubic Liénard equations
    • Lynch S. Generalized cubic Liénard equations. Appl Math Lett 12 (1999) 1-6
    • (1999) Appl Math Lett , vol.12 , pp. 1-6
    • Lynch, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.