Generating hidden hyperchaos in a 5D hyperchaotic Burke-Shaw system with three positive Lyapunov exponents
作者单位：School of Mathematics and Physics China University of Geosciences Division of Dynamics Technical University of Lodz College of Mechanical Engineering Beijing University of Technology Mathematical Institute University of Oxford Department of Physics University of Wisconsin
会议名称：《第十届动力学与控制学术会议》
会议日期：2016年
学科分类：07[理学] 070105[理学-运筹学与控制论] 070201[理学-理论物理] 0701[理学-数学] 0702[理学-物理学]
基 金：主持国家自然科学基金2项 主持中国博士后科学基金特别资助1项 主持中国博士后科学基金一等资助1项 主持北京市博士后科学基金1项 主持朝阳区博士后科学基金1项 主持湖北省自然科学基金面上资助项目1项 主持中国地质大学(武汉)中央高校基本科研业务费“摇篮计划”项目1项
关 键 词：Hidden attractor Hyperchaos No-equilibrium Stable equilibria Lyapunov exponents
摘 要：This paper reports the finding of hidden hyperchaos in a 5D hyperchaotic Burke-Shaw system, which is obtained by adding feedback controllers to the classic Burke-Shaw system. Of particular interest is that the hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed system with no equilibria or only two stable equilibria. The region of parameter space with bounded hidden solutions is relatively small, which accounts for the difficulty of surveying hidden attractors. Numerical analysis of phase trajectories, Lyapunov exponents, and Poincar′e map verify the existence of the hidden hyperchaotic attractors. As we know, the feature has not been previously reported in any other high dimensional system.Therefore it will represent a new type of hidden attractor with important and potentially problematic engineering consequences.