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**A hyperchaotic complex Chen system and its dynamics.**
*(English)*
Zbl 1136.37327

Summary: The main goal of this article is to introduce and study the dynamics of a new hyperchaotic complex Chen system. The dynamics of this system which is a 6-dimensional autonomous system is rich and complicated. The new system has chaotic, hyperchaotic attractors, periodic, quasi-periodic solutions and the solutions approach fixed points. These solutions are calculated based on Lyapunov exponents. Bifurcation diagram of this system are calculated and in good agreement with Lyapunov exponents. Different hyperchaotic complex Chen systems are suggested. Our results are demonstrated graphically.

### MSC:

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37C10 | Dynamics induced by flows and semiflows |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

34C28 | Complex behavior and chaotic systems of ordinary differential equations |

34C25 | Periodic solutions to ordinary differential equations |

34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |

34D20 | Stability of solutions to ordinary differential equations |