Abstract
The work in this paper consists of two parts. The one is modelling. After a method of classification for three dimensional (3D) autonomous chaotic systems and a concept of mixed Lorenz system are introduced, a mixed Lorenz system with a damped term is presented. The other is the analysis for dynamical properties of this model. First, its local stability and bifurcation in its parameter space are in detail considered. Then, the existence of its homoclinic and heteroclinic orbits, and the existence of singularly degenerate heteroclinic cycles, are studied by rigorous theoretical analysis. Finally, by using the Poincaré compactification for polynomial vector fields in
Funding source: NSF of China
Award Identifier / Grant number: 61473340
Funding source: NSF of Zhejiang University of Science and Technology
Award Identifier / Grant number: F701108G14
Funding source: Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province
Acknowledgments
This work is partly supported by NSF of China (grant: 61473340), NSF of Zhejiang University of Science and Technology (grant: F701108G14) and Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: NSF of China (grant: 61473340), NSF of Zhejiang University of Science and Technology (grant: F701108G14) and Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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