Some Dynamical Properties for New System derived From Chen and T Systems


In this paper we begin to study a nonlinear three dimensional continuous system with eight terms and three quadratic nonlinearities. The basic dynamical properties of the new system  are analyzed  by means of equilibrium point, stability and local bifurcations such as Pitchfork and Hopf bifurcations. Some of the basic dynamic behavior of the system is explored investigation in the Lyaponuv exponent, and we show that the new system is almost linear system.

Indexing terms/Keywords:

Chen system, T system, Hopf bifurcation, Stability, Lyaponuv exponent.


The science of nonlinear dynamics has sparked many researchers to develop mathematical models that simulate vector fields of nonlinear chaotic physical systems. Nonlinear phenomena arise in all fields of engineering, physics, chemistry, biology, economics, and sociology [1,2,3].

Chen and Ueta [4] constructed a three-dimensional autonomous differential equation with only two quadratic terms, xy and xz. In fact, Chen system has been proved to be dual to the Lorenz system [7,10], many theoretical analysis and numerical simulation results in [4,12,13]. The Chen system [4,9] which takes the form:


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About the Author

Hassan Kamil Jassim

Hassan Kamil Jassim, Ayed Elewise Hashoosh, Nabeel Jawad Hassan
Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq

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