Bridge the gap between the Lorenz system and the Chen system. (English) Zbl 1043.37026

Summary: This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
37N05 Dynamical systems in classical and celestial mechanics
70Q05 Control of mechanical systems
93B52 Feedback control
Full Text: DOI


[1] DOI: 10.1142/S0218127402005467 · Zbl 1043.37023 · doi:10.1142/S0218127402005467
[2] DOI: 10.1142/3033 · doi:10.1142/3033
[3] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[4] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[5] DOI: 10.1142/S0218127402004620 · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[6] DOI: 10.1142/S0218127402004851 · Zbl 1044.37021 · doi:10.1142/S0218127402004851
[7] DOI: 10.1142/S0218127402004735 · Zbl 1044.37022 · doi:10.1142/S0218127402004735
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