True and False Chaotic Attractors in a 3-D Lorenz-type System

Haijun Wang, Xianyi Li
2015 Annual Review of Chaos Theory, Bifurcations and Dynamical Systems  
In some known literatures those authors have analyzed the Yang system, x'=a(y-x), y'=cx-xz, z'=-bz+xy, containing three independent parameters. They think that they have found the system to have two interesting chaotic attractors (called as Yang-Chen attractor) when (a,b,c)=(10,8/3,16) and (a,b,c)=(35,3,35), respectively. However, by further analysis and Matlab simulation, we show that the two Yang--Chen chaotic attractors found are actually pseudo ones. In fact, the two attractors are locally
more » ... symptotically stable equilibria. Further, we present the values of parameters for this system to really generate chaotic attractor. Accordingly, we find a new attractor in the Yang system co-existing with one saddle and two stable node-foci.
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