Complexity Algorithms And Its Appalication In The Analyses Of The Enhanced Chaotic Systems

In this paper, the complexities of the enhanced chaotic systems (hyperchaotic Lorenz system, multi-wing Chen system and multi-scroll Chua system) are analyzed by employing a variety of complexity algorithms. The results have important theory meanings and practical applying value.FuzzyEn algorithm and SCM algorithm selected from behavior complexity algorithms and SE algorithm and C0algorithm selected from structure complexity algorithms are investigated, including the algorithms principle, the algorithm characteristics, parameters selecting rules and performance comparing among algorithms. Complexities of original sequences and pseudo-random sequences from the enhanced chaotic systems are analyzed by the the four complexity measure algorithms, respectively. Thus, complexities of the enhanced chaotic systems are analyzed from different angles. Complexity stability measure algorithms are also designed and studied, and the complexity stabilities of the enhanced chaotic systems are analyzed. The results illustrate that the hyperchaotic Lorenz system show the optimal complexity performance when the system is hyperchaotic; complexities of multi-wing chaotic systems decrease with the increase of wing number; complexities of multi-scroll chaotic system overall remain stable with the increase of scroll number, but the SE complexity variance stabilities are reduced; the complexities of the three systems in descending order are hyperchaotic Lorenz system, multi-wing Chen system and multi-scroll Chua system. The dynamical complexities such as the phase diagram, the energy spectrum structure are studied, and the results are consistent with the complexity measure results.A MATLAB complexity analysis toolbox is designed. A testing scheme of this toolbox is proposed and the testing results confirm that the design of the toolbox is reasonable and reliable.