Estimating the ultimate bound for the generalized quadratic autonomous chaotic systems

By using the optimization idea, this paper introduces a universal approach to estimate the ultimate bounds of the generalized quadratic autonomous chaotic systems (GQACS). Based on the proposed technique, a sufficient condition is then given to estimate the ultimate bounds of the GQACS. To validate the presented sufficient condition, one further estimates the ultimate bounds of a generalized Lorenz system and the hyperchaotic Lorenz-Stenflo system. It should be especially pointed out that our results include several well-known ultimate bound estimations as our special cases. Finally, several typical numerical examples are also given to visualize our theoretical results.