메뉴 건너뛰기




Volumn 16, Issue , 2005, Pages 1079-1084

An algorithm for computing heteroclinic orbits and its application to chaos synthesis in the generalized Lorenz system

Author keywords

Generalized Lorenz canonical form; Heteroclinic orbit; i'lnikov criterion

Indexed keywords

CHAOTIC OSCILLATION; GENERALIZED LORENZ CANONICAL FORM; GENERALIZED LORENZ SYSTEM; HETEROCLINIC ORBIT; HYPERBOLIC EQUILIBRIUMS; INVARIANT MANIFOLDS; ITS APPLICATIONS; UNIFORM CONVERGENCE;

EID: 79960714845     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00836     Document Type: Conference Paper
Times cited : (5)

References (24)
  • 1
    • 0036657932 scopus 로고    scopus 로고
    • Stability of observer-based chaotic communitcation for a class of Lur'e systems
    • Alvarez, J., Puebla, H. and Cervantes, I. (2002) Stability of observer-based chaotic communitcation for a class of Lur'e systems. Int. J. of Bifur. Chaos, 7, 1605-1618.
    • (2002) Int. J. of Bifur. Chaos , vol.7 , pp. 1605-1618
    • Alvarez, J.1    Puebla, H.2    Cervantes, I.3
  • 2
    • 0030405090 scopus 로고    scopus 로고
    • Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
    • Bai, F. & Champneys, A. R. (1996) Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two. Dynamics and Stability of Systems, 11(4), 325-346.
    • (1996) Dynamics and Stability of Systems , vol.11 , Issue.4 , pp. 325-346
    • Bai, F.1    Champneys, A.R.2
  • 4
    • 0036696341 scopus 로고    scopus 로고
    • On a generalized Lorenz canonical form of chaotic systems
    • Čelikovský, S. & Chen, G. (2002). On a generalized Lorenz canonical form of chaotic systems, Int. J. of Bifur. Chaos, 12, 1789-1812.
    • (2002) Int. J. of Bifur. Chaos , vol.12 , pp. 1789-1812
    • Čelikovský, S.1    Chen, G.2
  • 5
    • 0000863462 scopus 로고
    • Bilinear systems and chaos
    • Ccaronelikovský, S. & Vaneecaronccaronek, A. (1994). Bilinear systems and chaos. Kybernetika, 30, 403-424.
    • (1994) Kybernetika , vol.30 , pp. 403-424
    • Čelikovský, S.1    Vaněček, A.2
  • 6
    • 5544311017 scopus 로고
    • Existence of a homoclinic orbit of the Lorenz system by precise sgooting
    • Hassard B. & Zhang, J. (1994) Existence of a homoclinic orbit of the Lorenz system by precise sgooting. SIAM J. Math. Anal., 25(1), 179-196.
    • (1994) SIAM J. Math. Anal. , vol.25 , Issue.1 , pp. 179-196
    • Hassard, B.1    Zhang, J.2
  • 7
    • 18544393481 scopus 로고    scopus 로고
    • Periodic orbits and homoclinic orbits of the diffusionless Lorenz equations
    • Huang, D. B. (2003) Periodic orbits and homoclinic orbits of the diffusionless Lorenz equations. Physics Letter A, 309, 248-253.
    • (2003) Physics Letter A , vol.309 , pp. 248-253
    • Huang, D.B.1
  • 8
    • 0005229389 scopus 로고
    • A numerical method for finding homo-clinic orbits of Hamiltonian systems
    • Lassoued, L. & Mathlouthi, S. (1992) A numerical method for finding homo-clinic orbits of Hamiltonian systems. Numerical Functional Analysis and Optimization, 13(1-2), 155-172.
    • (1992) Numerical Functional Analysis and Optimization , vol.13 , Issue.1-2 , pp. 155-172
    • Lassoued, L.1    Mathlouthi, S.2
  • 9
    • 0000086970 scopus 로고
    • Homoclinic bifurcation to a transitive attractor of Lorenz type
    • Robinson, C. (1989) Homoclinic bifurcation to a transitive attractor of Lorenz type. Nonlinearity, 2, 495-518.
    • (1989) Nonlinearity , vol.2 , pp. 495-518
    • Robinson, C.1
  • 10
    • 0007251283 scopus 로고
    • Homoclinic bifurcation to a transitive attractor of Lorenz type, II
    • Robinson, C. (1992) Homoclinic bifurcation to a transitive attractor of Lorenz type, II. SIAM J. Math. Anal., 23(5), 1255-1268.
    • (1992) SIAM J. Math. Anal. , vol.23 , Issue.5 , pp. 1255-1268
    • Robinson, C.1
  • 11
    • 0034353690 scopus 로고    scopus 로고
    • Nonsymmetric Lorenz attractors from a homoclinic bifurcation
    • Robinson, C. (2000) Nonsymmetric Lorenz attractors from a homoclinic bifurcation. SIAM J. Math. Anal., 32(1), 119-141.
    • (2000) SIAM J. Math. Anal. , vol.32 , Issue.1 , pp. 119-141
    • Robinson, C.1
  • 12
    • 49549126801 scopus 로고    scopus 로고
    • An equation for continuous chaos
    • Rössler, O. E. (1996). An equation for continuous chaos, Phys. Lett. A, 57, 5:397-398.
    • (1996) Phys. Lett. A , vol.57 , Issue.5 , pp. 397-398
    • Rössler, O.E.1
  • 13
    • 0001234956 scopus 로고
    • A case of the existence of a countable number of periodic motions
    • Docklady, (translated by)
    • Ši'lnikov, L. P. (1965). A case of the existence of a countable number of periodic motions. Sov. Math. Docklady, 6, 163-166 (translated by S. Puckette).
    • (1965) Sov. Math. , vol.6 , pp. 163-166
    • Ši'lnikov, L.P.1    Puckette, S.2
  • 14
    • 84956230541 scopus 로고
    • A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddle-focus type
    • translated by
    • Ši'lnikov, L. P. (1970). A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddle-focus type. Math. U.S.S.R.-Shornik, 10, 91-102 (translated by F. A. Cezus).
    • (1970) Math. U.S.S.R.-Shornik , vol.10 , pp. 91-102
    • Ši'lnikov, L.P.1    Cezus, F.A.2
  • 17
    • 0033563546 scopus 로고    scopus 로고
    • C. R. Acad. Paris Ser. I Math
    • Tucker, W. (1999). The Lorenz attractor exists. C. R. Acad. Paris Ser. I Math., 328, 1197-1202.
    • (1999) The Lorenz Attractor Exists , vol.328 , pp. 1197-1202
    • Tucker, W.1
  • 18
    • 0032027324 scopus 로고    scopus 로고
    • Analytic approximation of the homoclinic orbits of the Lorenz system at σ = 10, b = 8/3, and ρ = 13.926
    • Vakakis, A. F. & Azeez, M. F. (1998) Analytic approximation of the homoclinic orbits of the Lorenz system at σ = 10, b = 8/3, and ρ = 13.926..., Nonlinear Dynamics, 15, 245-257.
    • (1998) Nonlinear Dynamics , vol.15 , pp. 245-257
    • Vakakis, A.F.1    Azeez, M.F.2
  • 21
    • 0942266242 scopus 로고    scopus 로고
    • A simple smooth chaotic system with a 3-layer attractor
    • Zhou, T. S. & Chen, G. (2004). A simple smooth chaotic system with a 3-layer attractor. Int. J. Bifur. Chaos, 14, 1795-1799.
    • (2004) Int. J. Bifur. Chaos , vol.14 , pp. 1795-1799
    • Zhou, T.S.1    Chen, G.2
  • 22
    • 0042623485 scopus 로고    scopus 로고
    • Constructing a new chaotic system based on Ši'lnikov criterion
    • Zhou, T. S., Chen, G. & Yang, Q. G. (2003). Constructing a new chaotic system based on Ši'lnikov criterion. Chaos, Solitons and Fractals, 19, 985- 993.
    • (2003) Chaos, Solitons and Fractals , vol.19 , pp. 985-993
    • Zhou, T.S.1    Chen, G.2    Yang, Q.G.3
  • 24
    • 15544370574 scopus 로고    scopus 로고
    • Shilnikov chaos in the generalized Lorenz canonical form of dynamical system
    • in press
    • Zhou, T., Chen, G. & Čelikovský, S. (2005) Shilnikov chaos in the generalized Lorenz canonical form of dynamical system. Nonlinear Dynamics, in press.
    • (2005) Nonlinear Dynamics
    • Zhou, T.1    Chen, G.2    Čelikovský, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.