Constructing a chaotic system with any number of equilibria

Nonlinear Dynamics

Volumn 71, Issue 3, 2013, Pages 429-436

  Wang, Xiong ^a   Chen, Guanrong ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Chaotic attractor; Chaotic system; Equilibrium; Stable chaos

Indexed keywords

CHAOTIC SYSTEMS; PHASE EQUILIBRIA;

CHAOTIC ATTRACTORS; CHAOTIC LORENZ SYSTEM; CHEN SYSTEM; DYNAMICAL BEHAVIORS; NEW CHAOTIC SYSTEMS; STABLE EQUILIBRIUM;

SYSTEM STABILITY;

EID: 84878695597     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0669-7     Document Type: Article

References (19)

1. Ovsyannikov, L., Šil'nikov, L.: On systems with a saddle-focus homoclinic curve. Sb. Math. 58(2), 557-574 (1987)
2. Šil'nikov, L.: A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Sb. Math. 10(1), 91-102 (1970)
3. Šil'nikov, A., Šil'nikov, L., Turaev, D.: Normal forms and Lorenz attractors. Int. J. Bifurc. Chaos 3, 1123 (1993)
4. Šilnikov, L., Šilnikov, A., Turaev, D.: Methods of Qualitative Theory in Nonlinear Dynamics. World Scientific, Singapore (2001)
5. Chen, B., Zhou, T., Chen, G.: An extended Šil'nikov homoclinic theorem and its applications. Int. J. Bifurc. Chaos 19, 1679-1693 (2009)
6. Sprott, J.C.: Automatic generation of strange attractors. Comput. Graph. 17, 325-332 (1993)
7. Sprott, J.C.: Some simple chaotic flows. Phys. Rev. E 50, 647-650 (1994)
8. Sprott, J.C.: Simplest dissipative chaotic flow. Phys. Lett. A 228, 271-274 (1997)
9. Sprott, J.C., Linz, S.J.: Algebraically simple chaotic flows. J. Chaos Theory Appl. 5, 3-22 (2000)
10. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963)
11. Ueta, T., Chen, G.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465-1466 (1999)
12. Ueta, T., Chen, G.: Bifurcation analysis of Chen's equation. Int. J. Bifurc. Chaos 10, 1917-1931 (2000)
13. Zhou, T., Chen, G., Čelikovský, S.: Šil'nikov chaos in the generalized Lorenz canonical form of dynamical systems. Nonlinear Dyn. 39(4), 319-334 (2005)
14. Li, T., Chen, G., Tang, Y., Yang, L.: Hopf bifurcation of the generalized Lorenz canonical form. Nonlinear Dyn. 47(4), 367-375 (2007)
15. Li, X., Ou, Q.: Dynamical properties and simulation of a new Lorenz-like chaotic system. Nonlinear Dyn. 65(3), 255-270 (2011)
16. Mu, C., Zhang, F., Shu, Y., Zhou, S.: On the boundedness of solutions to the Lorenz-like family of chaotic systems. Nonlinear Dyn. 67(2), 987-996 (2012)
17. Yang, Q., Chen, G.: A chaotic system with one saddle and two stable node-foci. Int. J. Bifurc. Chaos 18, 1393-1414 (2008)
18. Yang, Q., Wei, Z., Chen, G.: An unusual 3D autonomous quadratic chaotic system with two stable node-foci. Int. J. Bifurc. Chaos 20, 1061-1083 (2010)
19. Wang, X., Chen, G.: A chaotic system with only one stable equilibrium. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1264-1272 (2012)