On the Dynamics of the Unified Chaotic System Between Lorenz and Chen Systems

PublishedA 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

Heteroclinic, homoclinic and closed orbits in the Chen system

Bounded orbits such as closed, homoclinic and heteroclinic orbits are discussed in this work for a Lorenz- like 3D nonlinear system. For a large spectrum of the parameters the system has neither closed nor homoclinic orbits but has exactly two heteroclinic orbits, while under other constraints the system has symmetrical homoclinic orbits