메뉴 건너뛰기




Volumn 217, Issue 2, 2005, Pages 341-362

Convergence to equilibria in the Lorenz system via monotone methods

Author keywords

Convergence to equilibria; Invariant manifold; Lorenz system; Monotone flow

Indexed keywords


EID: 26844490163     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.08.005     Document Type: Article
Times cited : (12)

References (20)
  • 1
    • 0037095592 scopus 로고    scopus 로고
    • Massera's theorem for monotone dynamical systems in three dimensions
    • J. Campos Massera's theorem for monotone dynamical systems in three dimensions J. Math. Anal. Appl. 269 2002 607-615
    • (2002) J. Math. Anal. Appl. , vol.269 , pp. 607-615
    • Campos, J.1
  • 2
    • 0030540448 scopus 로고    scopus 로고
    • Lorenz equations. I. Existence and nonexistence of homoclinic orbits
    • X. Chen Lorenz equations. I. Existence and nonexistence of homoclinic orbits SIAM J. Math. Anal. 27 1996 1057-1069
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1057-1069
    • Chen, X.1
  • 3
    • 0011672661 scopus 로고    scopus 로고
    • Lorenz equations. II. Randomly rotated homoclinic orbits and chaotic trajectories
    • X. Chen Lorenz equations. II. Randomly rotated homoclinic orbits and chaotic trajectories Discrete Continuous Dynamical Systems 2 1996 121-140
    • (1996) Discrete Continuous Dynamical Systems , vol.2 , pp. 121-140
    • Chen, X.1
  • 6
    • 0042941238 scopus 로고    scopus 로고
    • Integrals of motion and the shape of the attractor for the Lorenz model
    • H. Giacomini S. Neukirch Integrals of motion and the shape of the attractor for the Lorenz model Phys. Lett. A 227 1997 309-318
    • (1997) Phys. Lett. A , vol.227 , pp. 309-318
    • Giacomini, H.1    Neukirch, S.2
  • 8
    • 0002220884 scopus 로고
    • A computer proof that the Lorenz equations have "chaotic" solutions
    • B. Hassard J. Zhang S.P. Hastings W.C. Troy A computer proof that the Lorenz equations have "chaotic" solutions Appl. Math. Lett. 7 1994 79-83
    • (1994) Appl. Math. Lett. , vol.7 , pp. 79-83
    • Hassard, B.1    Zhang, J.2    Hastings, S.P.3    Troy, W.C.4
  • 9
    • 0000356514 scopus 로고
    • A proof that the Lorenz equations have a homoclinic orbit
    • S.P. Hastings W.C. Troy A proof that the Lorenz equations have a homoclinic orbit J. Differential Equations 113 1994 166-188
    • (1994) J. Differential Equations , vol.113 , pp. 166-188
    • Hastings, S.P.1    Troy, W.C.2
  • 10
    • 0000885375 scopus 로고
    • Systems of differential equations which are competitive or cooperative I: Limit sets
    • M.W. Hirsch Systems of differential equations which are competitive or cooperative I Limit sets SIAM J. Appl. Math. 13 1982 167-179
    • (1982) SIAM J. Appl. Math. , vol.13 , pp. 167-179
    • Hirsch, M.W.1
  • 12
    • 0000241853 scopus 로고
    • Deterministic non-periodic flows
    • E.N. Lorenz Deterministic non-periodic flows J. Atmos. Sci. 20 1963 130-141
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 13
    • 0002403778 scopus 로고
    • Chaos in the Lorenz equations: A computer-assisted proof
    • K. Mischaikow M. Mrozek Chaos in the Lorenz equations a computer-assisted proof Bull. Amer. Math. Soc. 32 1995 66-72
    • (1995) Bull. Amer. Math. Soc. , vol.32 , pp. 66-72
    • Mischaikow, K.1    Mrozek, M.2
  • 15
    • 0036334349 scopus 로고    scopus 로고
    • An application of the theory of monotone systems to an electrical circuit
    • L.A. Sanchez An application of the theory of monotone systems to an electrical circuit Proc. Roy. Soc. Edinburgh 132A 2002 711-728
    • (2002) Proc. Roy. Soc. Edinburgh , vol.132 A , pp. 711-728
    • Sanchez, L.A.1
  • 16
    • 1842815853 scopus 로고    scopus 로고
    • Convergence in a Chua's system with three equilibria
    • L.A. Sanchez Convergence in a Chua's system with three equilibria Z. Angew. Math. Phys. 55 2004 183-200
    • (2004) Z. Angew. Math. Phys. , vol.55 , pp. 183-200
    • Sanchez, L.A.1
  • 17
    • 84971128384 scopus 로고
    • Some applications of Hausdorff dimensions inequalities for ordinary differential equations
    • R.A. Smith Some applications of Hausdorff dimensions inequalities for ordinary differential equations Proc. Roy. Soc. Edinburgh 104A 1986 235-259
    • (1986) Proc. Roy. Soc. Edinburgh , vol.104 A , pp. 235-259
    • Smith, R.A.1
  • 18
    • 0004068972 scopus 로고
    • New York: Springer
    • C. Sparrow The Lorenz Equations Bifurcations, Chaos and Strange Attractors 1982 Springer New York
    • (1982) The Lorenz Equations
    • Sparrow, C.1
  • 19
    • 0035911773 scopus 로고    scopus 로고
    • Bounds for trajectories of the Lorenz equations: An illustration of how to choose Liapunov functions
    • P. Swinnerton-Dyer Bounds for trajectories of the Lorenz equations: An illustration of how to choose Liapunov functions Phys. Lett. A 281 2001 161-167
    • (2001) Phys. Lett. A , vol.281 , pp. 161-167
    • Swinnerton-Dyer, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.