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In this paper, the stochastic resonance phenomenon in a tumor growth model under subthreshold periodic therapy and Lévy noise excitation is investigated. The possible reoccurrence of tumor due to stochastic resonance is discussed. The signal-to-noise ratio (SNR) is calculated numerically to measure the stochastic resonance. It is found that smaller stability index is better for avoiding tumor reappearance. Besides, the effect of the skewness parameter on the tumor regrowth is related to the stability index. Furthermore, increasing the intensity of periodic treatment does not always facilitate tumor therapy. These results are beneficial to the optimization of periodic tumor therapy.

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In this paper, we consider the response analysis of a Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed.