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Abstract
In this paper, we numerically analyze the effects of the time-delay feedback position, power noises, and fractional order on the peaks of antiperiodic oscillations (APOs) in a forced Duffing equation. It is found that the stability of the system depends on the sign of the gain coefficient about the delay. It is also found that the number, the shape, and the amplitude of the peaks of APO depend on the value of the time delay. When the system is subject to a stochastic perturbation, the number of peaks is not periodic. The effects of fractional order on the APOs are also studied. The results show that the number when the value of fractional-order derivative decreases, the number of the peaks of APO also decreases and the APO disappears for a certain value of fractional-order derivative.
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