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Bifurcation analysis of Chen’s equation. (English) Zbl 1090.37531

Summary: Anticontrol of chaos by making a nonchaotic system chaotic has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen’s equation, thereby revealing its different features from some other chaotic models such as its origin, the Lorenz system.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C23 Bifurcation theory for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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References:

[1] DOI: 10.1142/S0218127498001236 · Zbl 0941.93522 · doi:10.1142/S0218127498001236
[2] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[3] DOI: 10.1142/S0218127499000985 · Zbl 0964.93039 · doi:10.1142/S0218127499000985
[4] DOI: 10.1142/S0218127400001250 · doi:10.1142/S0218127400001250
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