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**A new series of three-dimensional chaotic systems with cross-product nonlinearities and their switching.**
*(English)*
Zbl 1266.34075

Summary: This paper introduces a new series of three-dimensional chaotic systems with cross-product nonlinearities. Based on some conditions, we analyze the globally exponentially or globally conditional exponentially attractive set and positive invariant set of these chaotic systems. Moreover, we give some known examples to show our results, and the exponential estimation is explicitly derived. Finally, we construct some three-dimensional chaotic systems with cross-product nonlinearities and study the switching system between them.

### MSC:

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

34D45 | Attractors of solutions to ordinary differential equations |

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\textit{X. Zhao} et al., J. Appl. Math. 2013, Article ID 590421, 14 p. (2013; Zbl 1266.34075)

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