Analytical and numerical investigation of a new Lorenz-like chaotic attractor with compound structures
This paper presents a three-dimensional autonomous Lorenz-like system formed by only five terms with a butterfly chaotic attractor. The dynamics of this new system is completely different from that in the Lorenz system family. This new chaotic system can display different dynamic behaviors such as periodic orbits, intermittency and chaos, which are numerically verified through investigating phase trajectories, Lyapunov exponents, bifurcation diagrams and Poincaré sections. Furthermore, this new system with compound structures is also proved by the presence of Hopf bifurcation at the equilibria and the crisis-induced intermittency.
KeywordsLorenz-like system Chaotic attractor Hopf bifurcation Crisis-induced intermittency Compound structures
This work was supported in part by the National Natural Science Foundation of China (Nos. 6117-4094 and 11202148), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20090031110029), the China/South Africa Research Cooperation Programme (Nos. 78673 and CS06-L02) and the South African National Research Foundation Incentive Grant (No. 81705).
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