多翼统一混沌系统的自适应同步及反同步

摘要

This paper investigated the synchronization and anti-synchronization of a new multi-wing unified chaotic system.The system combined the same structure of multi-wing system,and could produce different types of chaotic attractors by adjusting the system parameters.And it analyzed the dynamical characteristics of a new four-dimensional chaotic system,which could produce a kind of shape similar to that of a bat.Through the analysis and numerical simulation of the system's phase diagrams,Lyapunov exponent spectra and bifurcation diagrams,it shows that the system has an abundant chaotic behavior.Based on Lyapunov stability theory and adaptive control method,it gave the expression of nonlinear controller and the updating rule of parameters for the synchronization of the multi-wing unified chaotic system.Different dimensions of chaotic systems achieve antisynchronization in the add-dimension method.Eventually,it carried out the numerical simulations in MATLAB,the drive system and response system can quickly achieve the synchronization and anti synchronization,which verifies the effectiveness and feasibility of the proposed controllers and the parameter adaptive rate.%研究一种多翼统一混沌系统的同步及反同步问题.这种统一混沌系统将多种多翼混沌系统结合起来,通过调节系统参数可产生不同类型的混沌吸引子.分析多翼混沌系统中新发现的四维混沌系统的动力学特性,这种四维混沌系统可以产生一种形状似蝙蝠的吸引子.通过对新四维混沌系统的相图、李雅普诺夫指数谱和分岔图等动力学行为进行分析和数值仿真,验证了该系统具有丰富的混沌特性.通过Lyapunov稳定性理论和自适应控制方法,设计合适的非线性反馈控制器以及参数自适应率,实现该混沌系统的自适应同步.利用扩维的方法实现不同维数的非同族混沌系统间的自适应反同步.最后,在MATLAB中进行数值仿真,驱动系统和响应系统能快速达到同步和反同步,验证了上述方法的有效性和可行性.