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中文摘要：
首先给出了一个分数阶微分方程的定义和分数阶MAVPD混沌系统，在此系统之上，增加一个二次项yz，得到一个新的分数阶三维自治混沌系统，求出新混沌系统的不稳定平衡点．利用Routh—Hurwitz判据条件对平衡点进行分析，得到了使新混沌系统在不稳定平衡点实现稳定的条件，并以此为基础设计单变量反馈控制器，对该新分数阶混沌系统的不稳定平衡点进行控制．同时，还设计激活控制函数，得到该分数阶混沌系统自同步的充分条件，并应用拉普拉斯变换进行了理论证明，实现新分数阶混沌系统的自同步．最后，通过数值仿真，结果验证了新分数阶混沌系统在不稳定平衡点实现控制，同时也验证了该新分数阶混沌系统自同步理论的正确性．
英文摘要：
We give a definition of fractional-order differential equation, and a quadratic term yz is added based on the fractional-order modified autonomous van der Pol-Duffing（MAVPD） chaos system to help us get a new fractional three-dimensional autonomous chaos system. We solve the unstable equilibrium points of the new chaos system, and analyze its unstable equilibrium points using the Routh-Hurwitz criterion condition~ a stable condition that the new chaos system is stable in unstable equilibrium points is obtained~ based on it we design a single-variable feedback controller, to control over the unstable equilibrium points; simultaneously, by designing the activate control function, we gain the systemic simultaneous condition and apply the Laplace transformation theory to achieve the synchronization of the new system. Finally, by numerical simulation, the result proves that we achieve control and synchronization of the new fractionalorder chaotic system.
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