时不变分数阶系统反周期解的存在性

On the Existence of Anti-Periodic Solutions in Time-Invariant Fractional Order Systems

反周期解问题是非线性微分系统动力学的重要特征.近年来,非线性整数阶微分系统的反周期解问题得到了广泛的研究,非线性分数阶微分系统的反周期解问题也得到了初步的讨论.不同于已有的工作,该文研究时不变分数阶系统反周期解的存在性问题.证明了时不变分数阶系统在有限时间区间内不存在反周期解,而当分数阶导数的下限趋近于无穷大时,时不变分数阶系统却存在反周期解.

The anti-periodic solution problem makes an important characteristic of dynamics for nonlinear differential systems. In recent years, the anti-periodic solution problem in integer order nonlinear differential systems had been widely studied, while the anti-periodic solution problem in fractional order nonlinear differential systems had been preliminarily discussed. Oth- er than the previous work, the existence of anti-periodic solutions in time-invariant fractional order systems was investigated. It is shown that although within a finite time interval the solu- tions do not show any anti-periodic behavior, when the lower limit of the fractional order derivative tends to infinity the anti-periodic orbits will be obtained.