On a four-dimensional chaotic system. (English) Zbl 1071.37025

Summary: This paper reports a new four-dimensional continuous autonomous chaotic system, in which each equation in the system contains a 3-term cross product. Basic properties of the system are analyzed by means of Lyapunov exponents and bifurcation diagrams.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
Full Text: DOI


[1] Sparrow, C., The Lorenz equations: bifurcations, chaos, and strange attractors, (1982), Springer-Verlag NY · Zbl 0504.58001
[2] Rösslor, O.E., An equation for continuous chaos, Phys. lett. A, 57, 397-398, (1976) · Zbl 1371.37062
[3] Chen, G., Chaotification via feedback: the discrete case, (), 159-177 · Zbl 1330.93107
[4] Chen, G.; Ueta, T., Yet another chaotic attractor, Int. J. bifurcat. chaos, 9, 1465-1466, (1999) · Zbl 0962.37013
[5] Ueta, T.; Chen, G., Bifurcation analysis of chen’s equation, Int. J. bifurcat. chaos, 10, 1917-1931, (2000) · Zbl 1090.37531
[6] Liu, W.B.; Chen, G., A new chaotic system and its generation, Int. J. bifurcat. chaos, 13, 261-267, (2003) · Zbl 1078.37504
[7] Lü, J.H.; Chen, G., A new chaotic attractor coined, Int. J. bifurcat. chaos, 12, 659-661, (2002) · Zbl 1063.34510
[8] Lü, J.H.; Chen, G.; Celikovský, S., Bridge the gap between the Lorenz system and the Chen system, Int. J. bifurcat. chaos, 12, 2917-2926, (2002) · Zbl 1043.37026
[9] Vanecek, A.; Celikovský, S., Control systems: from linear analysis to synthesis of chaos, (1996), Prentice-Hall London · Zbl 0874.93006
[10] Wang, X.F., Generating chaos in continuous-time systems via feedback control, (), 179-204 · Zbl 1043.93027
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