메뉴 건너뛰기




Volumn 243, Issue , 2014, Pages 12-23

Boundedness solutions of the complex Lorenz chaotic system

Author keywords

Generalized Lyapunov functions; Global attractive set; Lorenz system

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL TECHNIQUES;

EID: 84902678450     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.05.102     Document Type: Article
Times cited : (31)

References (32)
  • 1
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E.N. Lorenz Deterministic nonperiodic flow J. Atmos. Sci. 20 1963 130 141
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 2
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O.E. Rossler An equation for continuous chaos Phys. Lett. A 57 1976 397 398
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rossler, O.E.1
  • 5
    • 33846540826 scopus 로고    scopus 로고
    • Hopf bifurcation of the generalized Lorenz canonical form
    • DOI 10.1007/s11071-006-9036-x
    • T. Li, G. Chen, Y. Tang, and L. Yang Hopf bifurcation of the generalized Lorenz canonical form Nonlinear Dyn. 47 4 2007 367 375 (Pubitemid 46154544)
    • (2007) Nonlinear Dynamics , vol.47 , Issue.4 , pp. 367-375
    • Li, T.1    Chen, G.2    Tang, Y.3    Yang, L.4
  • 6
    • 84888342556 scopus 로고    scopus 로고
    • Bounds of solutions of a kind of hyper-chaotic systems and application
    • F. Zhang, Y. Li, and C. Mu Bounds of solutions of a kind of hyper-chaotic systems and application J. Math. Res. Appl. 33 3 2013 345 352
    • (2013) J. Math. Res. Appl. , vol.33 , Issue.3 , pp. 345-352
    • Zhang, F.1    Li, Y.2    Mu, C.3
  • 7
    • 84855782778 scopus 로고    scopus 로고
    • On the boundedness of solutions to the Lorenz-like family of chaotic systems
    • C. Mu, F. Zhang, Y. Shu, and S. Zhou On the boundedness of solutions to the Lorenz-like family of chaotic systems Nonlinear Dyn. 67 2 2012 987 996
    • (2012) Nonlinear Dyn. , vol.67 , Issue.2 , pp. 987-996
    • Mu, C.1    Zhang, F.2    Shu, Y.3    Zhou, S.4
  • 8
    • 84878695597 scopus 로고    scopus 로고
    • Constructing a chaotic system with any number of equilibria
    • X. Wang, and G. Chen Constructing a chaotic system with any number of equilibria Nonlinear Dyn. 71 3 2013 429 436
    • (2013) Nonlinear Dyn. , vol.71 , Issue.3 , pp. 429-436
    • Wang, X.1    Chen, G.2
  • 9
    • 84888375546 scopus 로고    scopus 로고
    • On the new results of global exponential attractive set
    • F. Zhang, C. Mu, L. Wang, G. Zhang, and I. Ahmed On the new results of global exponential attractive set Appl. Math. Lett. 28 2014 30 37
    • (2014) Appl. Math. Lett. , vol.28 , pp. 30-37
    • Zhang, F.1    Mu, C.2    Wang, L.3    Zhang, G.4    Ahmed, I.5
  • 10
    • 84893836047 scopus 로고    scopus 로고
    • Estimations for ultimate boundary of a new hyperchaotic system and its simulation
    • F. Zhang, C. Mu, L. Wang, X. Wang, and X. Yao Estimations for ultimate boundary of a new hyperchaotic system and its simulation Nonlinear Dyn. 75 2014 529 537
    • (2014) Nonlinear Dyn. , vol.75 , pp. 529-537
    • Zhang, F.1    Mu, C.2    Wang, L.3    Wang, X.4    Yao, X.5
  • 11
    • 84868088152 scopus 로고    scopus 로고
    • General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
    • G. Leonov General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems Phys. Lett. A 376 2012 3045 3050
    • (2012) Phys. Lett. A , vol.376 , pp. 3045-3050
    • Leonov, G.1
  • 12
    • 4544372373 scopus 로고    scopus 로고
    • Lyapunov dimension formulas for Henon and Lorenz attractors
    • G. Leonov Lyapunov dimension formulas for Henon and Lorenz attractors St. Petersburg Math. J. 13 2001 1 12
    • (2001) St. Petersburg Math. J. , vol.13 , pp. 1-12
    • Leonov, G.1
  • 13
    • 79956081226 scopus 로고    scopus 로고
    • Localization of hidden Chua's attractors
    • G. Leonov, N. Kuznetsov, and V. Vagaitsev Localization of hidden Chua's attractors Phys. Lett. A 375 2011 2230 2233
    • (2011) Phys. Lett. A , vol.375 , pp. 2230-2233
    • Leonov, G.1    Kuznetsov, N.2    Vagaitsev, V.3
  • 14
    • 84964265507 scopus 로고    scopus 로고
    • Analytical-numerical methods for hidden attractors' localization: The 16th Hilbert problem, Aizerman and Kalman conjectures, and Chua circuits, numerical methods for differential equations, optimization, and technological problems
    • G. Leonov, and N. Kuznetsov Analytical-numerical methods for hidden attractors' localization: the 16th Hilbert problem, Aizerman and Kalman conjectures, and Chua circuits, numerical methods for differential equations, optimization, and technological problems Comput. Methods Appl. Sci. 27 2013 41 64
    • (2013) Comput. Methods Appl. Sci. , vol.27 , pp. 41-64
    • Leonov, G.1    Kuznetsov, N.2
  • 15
    • 84874642094 scopus 로고    scopus 로고
    • Hidden attractors in dynamical systems. from hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits
    • G. Leonov, and N. Kuznetsov Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits Int. J. Bifurc. Chaos Appl. Sci. Eng. 23 2013 1330002
    • (2013) Int. J. Bifurc. Chaos Appl. Sci. Eng. , vol.23 , pp. 1330002
    • Leonov, G.1    Kuznetsov, N.2
  • 16
    • 80052988208 scopus 로고    scopus 로고
    • Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
    • V. Bragin, V. Vagaitsev, N. Kuznetsov, and G. Leonov Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits J. Comput. Syst. Sci. Int. 50 2011 511 543
    • (2011) J. Comput. Syst. Sci. Int. , vol.50 , pp. 511-543
    • Bragin, V.1    Vagaitsev, V.2    Kuznetsov, N.3    Leonov, G.4
  • 18
    • 84984076276 scopus 로고
    • Attractor localization of the Lorenz system
    • G. Leonov, A. Bunin, and N. Koksch Attractor localization of the Lorenz system Z. Angew. Math. Mech. 67 1987 649 656
    • (1987) Z. Angew. Math. Mech. , vol.67 , pp. 649-656
    • Leonov, G.1    Bunin, A.2    Koksch, N.3
  • 19
    • 79952290511 scopus 로고    scopus 로고
    • Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization
    • F. Zhang, Y. Shu, H. Yang, and X. Li Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization Chaos, Solitons Fractals 44 1-3 2011 137 144
    • (2011) Chaos, Solitons Fractals , vol.44 , Issue.13 , pp. 137-144
    • Zhang, F.1    Shu, Y.2    Yang, H.3    Li, X.4
  • 20
    • 77957344292 scopus 로고    scopus 로고
    • Bounds for a new chaotic system and its application in chaos synchronization
    • F. Zhang, Y. Shu, and H. Yang Bounds for a new chaotic system and its application in chaos synchronization Commun. Nonlinear Sci. Numer. Simul. 16 3 2011 1501 1508
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , Issue.3 , pp. 1501-1508
    • Zhang, F.1    Shu, Y.2    Yang, H.3
  • 21
    • 62949192764 scopus 로고    scopus 로고
    • Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system
    • D. Li, X. Wu, and J. Lu Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system Chaos, Solitons Fractals 39 2009 1290 1296
    • (2009) Chaos, Solitons Fractals , vol.39 , pp. 1290-1296
    • Li, D.1    Wu, X.2    Lu, J.3
  • 22
    • 84862793585 scopus 로고    scopus 로고
    • On the boundness of some solutions of the Lü system
    • F. Zhang, C. Mu, and X. Li On the boundness of some solutions of the Lü system Int. J. Bifurc. Chaos 22 1 2012 1 5
    • (2012) Int. J. Bifurc. Chaos , vol.22 , Issue.1 , pp. 1-5
    • Zhang, F.1    Mu, C.2    Li, X.3
  • 23
    • 64949138913 scopus 로고    scopus 로고
    • Solution bounds of generalized Lorenz chaotic systems
    • Y. Sun Solution bounds of generalized Lorenz chaotic systems Chaos, Solitons Fractals 40 2009 691 696
    • (2009) Chaos, Solitons Fractals , vol.40 , pp. 691-696
    • Sun, Y.1
  • 25
    • 40549096015 scopus 로고    scopus 로고
    • Active control and global synchronization of the complex chen and Lü systems
    • DOI 10.1142/S0218127407019962, PII S0218127407019962
    • G.M. Mahmoud, T. Bountis, and E.E. Mahmoud Active control and global synchronization for complex Chen and Lü systems Int. J. Bifurc. Chaos 17 2007 4295 4308 (Pubitemid 351365913)
    • (2007) International Journal of Bifurcation and Chaos , vol.17 , Issue.12 , pp. 4295-4308
    • Mahmoud, G.M.1    Bountis, T.2    Mahmoud, E.E.3
  • 26
    • 80052032851 scopus 로고    scopus 로고
    • Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters
    • S. Liu, and P. Liu Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters Nonlinear Anal. Real World Appl. 12 2011 3046 3055
    • (2011) Nonlinear Anal. Real World Appl. , vol.12 , pp. 3046-3055
    • Liu, S.1    Liu, P.2
  • 28
    • 84888374097 scopus 로고    scopus 로고
    • Characteristics of time-delay complex Lorenz chaotic system and its self-synchronization of time delay
    • F. Zhang, S. Liu, and W. Yu Characteristics of time-delay complex Lorenz chaotic system and its self-synchronization of time delay Acta Phys. Sin. 62 22 2013 220505
    • (2013) Acta Phys. Sin. , vol.62 , Issue.22 , pp. 220505
    • Zhang, F.1    Liu, S.2    Yu, W.3
  • 29
    • 34250157760 scopus 로고    scopus 로고
    • Time-varying linearization and the perron effects
    • DOI 10.1142/S0218127407017732, PII S0218127407017732
    • G. Leonov, and N. Kuznetsov Time-varying linearization and the Perron effects Int. J. Bifurc. Chaos Appl. Sci. Eng. 17 2007 1079 1107 (Pubitemid 46905045)
    • (2007) International Journal of Bifurcation and Chaos , vol.17 , Issue.4 , pp. 1079-1107
    • Leonov, G.A.1    Kuznetsov, N.V.2
  • 30
    • 84886303693 scopus 로고    scopus 로고
    • Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor
    • N. Kuznetsov, T. Mokaev, and P. Vasilyev Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor Commun. Nonlinear Sci. Numer. Simul. 19 4 2014 1027 1034
    • (2014) Commun. Nonlinear Sci. Numer. Simul. , vol.19 , Issue.4 , pp. 1027-1034
    • Kuznetsov, N.1    Mokaev, T.2    Vasilyev, P.3
  • 31
    • 33746711700 scopus 로고    scopus 로고
    • On stability by the first approximation for discrete systems
    • DOI 10.1109/PHYCON.2005.1514053, 1514053, 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings
    • N. Kuznetsov, G. Leonov, On stability by the first approximation for discrete systems, in: 2005 International Conference on Physics and Control, 2005, PhysCon 2005, Proceedings 2005, (1514053), 2005 pp. 596-599. (Pubitemid 44160099)
    • (2005) 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings , vol.2005 , pp. 596-599
    • Kuznetsov, N.V.1    Leonov, G.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.