On the Dynamics of the Unified Chaotic System Between Lorenz and Chen Systems
International Journal of Bifurcation and Chaos
World Scientific Publishing
This is the author's accepted manuscript. The final version is available from World Scientific via the DOI in this record.
Reason for embargo
A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.
The first author is partially supported by a MINECO/FEDER grant MTM2008-03437 and MTM2013-40998-P, an AGAUR grant number 2014SGR-568, an ICREA Academia, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338, and UNAB 13-4E-1604.
Vol. 25, No. 9,
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