A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family. (English) Zbl 1221.37047
Summary: We give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz systems studied so far in the literature. The system considered in this paper not only contains the classical Lorenz system and the generalized Lorenz family as special cases, but also provides three new Lorenz systems, which do not belong to the generalized Lorenz system, but the general Lorenz system. The results presented in this paper contain all the existing relative results as special cases.
MSC:
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 34D45 | Attractors of solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
general Lorenz family; globally exponentially attractive set; positive invariant set; generalized Lyapunov function; ultimate boundedness of chaotic systemReferences:
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