×

Chaotic attractors of the conjugate Lorenz-type system. (English) Zbl 1149.37308

A new conjugate Lorenz-type system is introduced in this paper. The system contains as special cases the conjugate Lorenz system, conjugate Chen system and conjugate Lü system. Chaotic dynamics of the system in the parametric space is numerically and thoroughly investigated. Meanwhile, a set of conditions for possible existence of chaos are derived, which provide some useful guidelines for searching chaos in numerical simulations. Furthermore, some basic dynamical properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions and the compound structure of the system are demonstrated with various numerical examples.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Banks S. P., Int. J. Bifurcation and Chaos 8 pp 1–
[2] DOI: 10.1142/S0218127499001097 · Zbl 1192.37039
[3] Barnett S., Polynomials and Linear Control Systems (1983) · Zbl 0528.93003
[4] Celikovský S., Kybernetika 30 pp 403–
[5] Celikovský S., Control Systems: From Linear Analysis to Synthesis of Chaos (1996)
[6] DOI: 10.1142/S0218127402005467 · Zbl 1043.37023
[7] DOI: 10.1016/j.chaos.2005.02.040 · Zbl 1100.37016
[8] DOI: 10.1142/3033
[9] Chen G., Controlling Chaos and Bifurcations in Engineer System (1999)
[10] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013
[11] Hao B. L., Chaos (1984) · Zbl 0559.58012
[12] Lian K., IEEE Trans. Circ. Syst.-I 47 pp 1418–
[13] DOI: 10.1016/j.chaos.2003.10.009 · Zbl 1045.37014
[14] DOI: 10.1142/S0218127404009715 · Zbl 1129.37322
[15] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129
[16] DOI: 10.1142/S0218127402004620 · Zbl 1063.34510
[17] DOI: 10.1142/S021812740200631X · Zbl 1043.37026
[18] DOI: 10.1063/1.1478079
[19] DOI: 10.1142/S021812740401014X · Zbl 1129.37323
[20] DOI: 10.1090/S0273-0979-1995-00558-6 · Zbl 0820.58042
[21] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501
[22] DOI: 10.1016/j.physa.2004.12.040
[23] DOI: 10.1142/S0218127493000933 · Zbl 0885.58080
[24] DOI: 10.1016/0375-9601(80)90466-1
[25] DOI: 10.1007/978-1-4612-5767-7
[26] DOI: 10.1142/S0218127499001383 · Zbl 1089.37512
[27] DOI: 10.1016/S0764-4442(99)80439-X · Zbl 0935.34050
[28] Ueta T., Int. J. Bifurcation and Chaos 10 pp 1917–
[29] DOI: 10.1142/S0218127406016501 · Zbl 1185.37088
[30] DOI: 10.1142/S0218127403008089 · Zbl 1046.37018
[31] DOI: 10.1016/S0960-0779(03)00251-0 · Zbl 1053.37015
[32] DOI: 10.1142/S0218127404010175 · Zbl 1129.37325
[33] DOI: 10.1142/S0218127404011296 · Zbl 1129.37326
[34] DOI: 10.1007/s11071-005-4195-8 · Zbl 1142.70012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.