Nonlinear analysis in a Lorenz-like system

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 5, 2010, Pages 3491-3500

  Dias, Fabio Scalco ^a   Mello, Luis Fernando ^a   Zhang, Jian Gang ^b  

^a Universidade Federal de Itajub   (Brazil)

^b LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Hopf bifurcations; Limit cycles; Lyapunov coefficients; Singularly degenerate heteroclinic cycles

Indexed keywords

CHAOTIC ATTRACTORS; HETEROCLINIC CYCLES; LIMIT CYCLE; LYAPUNOV COEFFICIENT; NON-LINEAR DYNAMICS; QUADRATIC CHAOTIC SYSTEMS; SINGULARLY DEGENERATE HETEROCLINIC CYCLES; STABILITY AND BIFURCATION; THREE PARAMETERS;

HOPF BIFURCATION; NONLINEAR ANALYSIS;

CHAOTIC SYSTEMS;

EID: 77955512357     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.12.010     Document Type: Article

References (26)

1. E.N. Lorenz Deterministic nonperiodic flow J. Atmospheric Sci. 20 1963 130 141
2. C. Sparrow The Lorenz Equations: Bifurcations, Chaos and Strange Attractors 1982 SpringerVerlag New York
3. G. Chen, and T. Ueta Yet another chaotic attractor Internat. J. Bifur. Chaos 9 1999 1465 1466
4. C. Liu, T. Liu, L. Liu, and K. Liu A new chaotic attractor Chaos Solitons Fractals 22 2004 1031 1038
5. E. Rssler An equation for continuous chaos Phys. Lett. A 57 1976 397 398
6. T. Rikitake Oscillations of a system of disk dynamos Proc. R. Cambridge Philos. Soc. 54 1958 89 105
7. J. L, and G. Chen A new chaotic attractor coined Internat. J. Bifur. Chaos 12 2002 659 661
8. R. Genesio, and A. Tesi Harmonic balance methods for analysis of chaotic dynamics in nonlinear systems Automatica 28 1992 531 548
9. L.O. Chua Chua's circuit. An overview ten years later J. Circuits Syst. Comput. 4 1994 117 159
10. S. Gao, Z. Teng, J.J. Nieto, and A. Torres Analysis of an SIR epidemic model with pulse vaccination and distributed time delay J. Biomed. Biotechnol. 2007 2007 Article ID 64870
11. H. Zhang, L. Chen, and J.J. Nieto A delayed epidemic model with stage-structure and pulses for pest management strategy Nonlinear Anal. RWA 9 2008 1714 1726
12. L.F. Mello, and S.F. Coelho Degenerate Hopf bifurcations in the L system Phys. Lett. A 373 2009 1116 1120
13. L.F. Mello, M. Messias, and D.C. Braga Bifurcation analysis of a new Lorenz-like chaotic system Chaos Solitons Fractals 37 2008 1244 1255
14. J. calle Introduction aux functions analysables et preuve constructive de la conjecture de Dulac 1992 Hermann Paris (in French)
15. Y. Ilyashenko Finiteness Theorems for Limit Cycles 1993 American Mathematical Society Providence, RI
16. A. Ferragut, J. Llibre, C. Pantazi, Polynomial vector fields in R 3 with infinitely many limit cycles, preprint
17. X.-F. Li, Y.-D. Chu, J.-G. Zhang, and Y.-X. Chang Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor Chaos Solitons Fractals 41 2009 2360 2370
18. H. Kokubu, and R. Roussarie Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences: Part I J. Dynam. Differential Equations 16 2004 513 557
19. M. Messias Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system J. Phys. A: Math. Theor. 42 2009 115101
20. L.S. Pontryagin Ordinary Differential Equations 1962 Addison-Wesley Publishing Company Inc. Reading
21. Y.A. Kuznetsov Elements of Applied Bifurcation Theory second ed. 1998 Springer-Verlag New York
22. J. Sotomayor, L.F. Mello, and D.C. Braga Bifurcation analysis of the Watt governor system Comput. Appl. Math. 26 2007 19 44
23. J. Sotomayor, L.F. Mello, and D.C. Braga Hopf bifurcations in a Watt governor with a spring J. Nonlinear Math. Phys. 15 2008 278 289
24. Y.-D. Chu, J.-G. Zhang, X.-F. Li, Y.-X. Chang, and G.-W. Luo Chaos and chaos synchronization for a non-autonomous rotational machine systems Nonlinear Anal. RWA 9 2008 1378 1393
25. A. Wolf, J. Swift, H. Swinney, and J. Vastano Determining Lyapunov exponents from a time series Physica D 16 1985 285 317
26. Q. Yang, and G. Chen A chaotic system with one saddle and two stable node-foci Internat. J. Bifur. Chaos 18 2008 1393 1414