A fully qualified four-wing four-dimensional autonomous chaotic system and its synchronization

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• 作者：Fei Yu^a ; ^{yufeiyfyf@163.com} ; Lei Gao^a ; Ke Gu^a ; Bo Yin^a ; Qiuzhen Wan^b ; Zhili Zhou^c
• 关键词：Four-wing chaotic system ; Bifurcation diagram ; Lyapunov exponent spectrum ; Circuit implementation ; Synchronization
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：131
• 期：Complete
• 页码：79-88
• 全文大小：1759 K
• 卷排序：131

文摘

In order to generate a real four-wing chaotic attractor, a new four-dimensional (4D) smooth quadratic autonomous system which is constructed by a linear controller to a three-dimensional (3D) pseudo four-wing system is proposed in this paper. Some complex dynamical behaviors such as equilibrium points and chaos are investigated and analyzed. The corresponding four-wing chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation diagram, analysis of power spectrum and Poincaré maps. Furthermore, an oscillator circuit is designed for implementation, with Multisim observations for verification and demonstration. Finally, an extended synchronization approach is proposed for synchronizing the four-wing chaotic system. On the basis of Jacobin matrix method, it is not necessary to construct the Lyapunov functions, which makes this scheme simpler. Theoretical analysis and numerical simulations demonstrate the validity and feasibility of the proposed control method.