Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension

Ultimate bound estimation of chaotic systems is a difficult yet interesting mathematical question. At present, explicit ultimate bound sets can be analytically obtained only for some special chaotic systems, and few results are known for hyper-chaotic ones. In this paper, through the Lagrange multiplier method and set operations, one derives two kinds of explicit ultimate bound sets for a novel hyperchaotic system. Based on the estimated result and optimization method, one further estimates the Hausdorff dimension of the hyperchaotic attractor. Numerical simulations show the effectiveness and correctness of the conclusions. The investigations enrich the related results for the hyperchaotic systems, and provide support for the assertion: hyperchaotic systems are ultimately bounded.