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Wang, Pei; Li, Damei; Wu, Xiaoqun; Lü, Jinhu; Yu, Xinghuo

Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems. (English) Zbl 1248.34084

Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 9, 2679-2694 (2011).
Summary: This paper aims to propose a unified approach for the ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems (HDQADS). Using the proposed method and the optimization idea, a sufficient condition is then given for estimating the ultimate bounds of a class of HDQADS. To validate the above sufficient condition, this paper further investigates the ultimate bound estimation of a hyperchaotic system, a 6D and a 9D chaotic system, separately. Moreover, the ultimate bounds for a general Lorenz system, a low-order atmospheric circulation model, and a new 3D chaotic system are also discussed in detail. In particular, it should be pointed out that a unified and accurate ultimate bound estimation is attained for the generalized Lorenz system and it includes several well-known results as its special cases. Some numerical simulations are also given to verify and visualize the corresponding theoretical results.

Cited in 1 Review
Cited in 28 Documents

MSC:

34D45 Attractors of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations

Keywords:

ultimate bound estimation; high dimensional quadratic autonomous systems; chaos; optimization
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\textit{P. Wang} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 9, 2679--2694 (2011; Zbl 1248.34084)
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