메뉴 건너뛰기




Volumn 56, Issue 5, 2004, Pages 643-677

Necessary conditions for a limit cycle and its basin of attraction

Author keywords

Autonomous ordinary differential equation; Basin of attraction; Dynamical system; Periodic orbit

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

EID: 0346008096     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2003.07.020     Document Type: Article
Times cited : (22)

References (13)
  • 1
    • 0142239162 scopus 로고
    • A condition for the existence of orbitally stable solutions of dynamical systems
    • Borg G. A condition for the existence of orbitally stable solutions of dynamical systems. Kungl. Tekn. Högsk. Handl. 153:1960.
    • (1960) Kungl. Tekn. Högsk. Handl. , vol.153
    • Borg, G.1
  • 3
    • 0347329306 scopus 로고    scopus 로고
    • Unbounded Basins of Attraction of Limit Cycles
    • Giesl P. Unbounded Basins of Attraction of Limit Cycles. Acta Math. Univ. Comenianae. 72(1):2003;81-110.
    • (2003) Acta Math. Univ. Comenianae , vol.72 , Issue.1 , pp. 81-110
    • Giesl, P.1
  • 6
    • 84968520692 scopus 로고
    • On global asymptotic stability of solutions of differential equations
    • Hartman P., Olech C. On global asymptotic stability of solutions of differential equations. Trans. Amer. Math. Soc. 104:1962;154-178.
    • (1962) Trans. Amer. Math. Soc. , vol.104 , pp. 154-178
    • Hartman, P.1    Olech, C.2
  • 7
    • 0346698870 scopus 로고
    • A criterion for the strong orbital stability of the trajectories of dynamical systems I
    • Kravchuk A.Yu., Leonov G.A., Ponomarenko D.V. A criterion for the strong orbital stability of the trajectories of dynamical systems I. Differents. Uravn. 28(9):1992;1507-1520.
    • (1992) Differents. Uravn. , vol.28 , Issue.9 , pp. 1507-1520
    • Kravchuk, A.Yu.1    Leonov, G.A.2    Ponomarenko, D.V.3
  • 9
    • 0035371937 scopus 로고    scopus 로고
    • Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization
    • Leonov G.A., Noack A., Reitmann V. Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization. Nonlinear Anal. 44:2001;1057-1085.
    • (2001) Nonlinear Anal. , vol.44 , pp. 1057-1085
    • Leonov, G.A.1    Noack, A.2    Reitmann, V.3
  • 10
    • 0002760968 scopus 로고
    • Local instability and localization of attractors, from stochastic generator to Chua's systems
    • Leonov G.A., Ponomarenko D.V., Smirnova V.B. Local instability and localization of attractors, from stochastic generator to Chua's systems. Acta Appl. Math. 40:1995;179-243.
    • (1995) Acta Appl. Math. , vol.40 , pp. 179-243
    • Leonov, G.A.1    Ponomarenko, D.V.2    Smirnova, V.B.3
  • 11
    • 0347329301 scopus 로고
    • Dynamical systems with a certain local contraction property
    • Stenström B. Dynamical systems with a certain local contraction property. Math. Scand. 11:1962;151-155.
    • (1962) Math. Scand. , vol.11 , pp. 151-155
    • Stenström, B.1
  • 12
    • 0346068064 scopus 로고
    • Moving orthonormal system along a closed path of an autonomous system
    • Urabe M. Moving orthonormal system along a closed path of an autonomous system. J. Sci. Hiroshima Univ. Ser. A. 21:1958;177-192.
    • (1958) J. Sci. Hiroshima Univ. Ser. A , vol.21 , pp. 177-192
    • Urabe, M.1
  • 13
    • 0003264465 scopus 로고
    • Theory of Limit Cycles
    • AMS 66, American Mathematical Society, Providence, RI
    • Y. Ye, et al., Theory of Limit Cycles, Translations of Mathematical Monographs, AMS 66, American Mathematical Society, Providence, RI, 1986.
    • (1986) Translations of Mathematical Monographs
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.