Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 21, Issue 9, Pages 2679-2694Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127411030027
Keywords
Ultimate bound estimation; high dimensional quadratic autonomous systems; chaos; optimization
Funding
- National Natural Science Foundation of China [60821091, 60804039, 11072254, 61025017]
- National Basic Research (973) Program of China [2007CB310805]
- Australian Research Council (ARC) [FT0992226]
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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.
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