This paper aims to investigate the stochastic resonance （SR） in an FitzHugh-Nagumo （FHN） model with an additive LEvy noise numerically. The non-Gaussian LEvy noise is a kind of general random noise which is differ...This paper aims to investigate the stochastic resonance （SR） in an FitzHugh-Nagumo （FHN） model with an additive LEvy noise numerically. The non-Gaussian LEvy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio （SNR）, and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the LEvy noise and the FHN model on the SR will be exam- ined, and some mechanisms of the LEvy noise-induced SR are presented which are different from those of the Gaussian noise.展开更多
The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expres...The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.展开更多
Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resona...Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.展开更多
基金supported by the the National Natural Science Foundation of China(Grant Nos.11372247&11472224)the NPU Foundation for Undergraduate Graduation Design
文摘This paper aims to investigate the stochastic resonance （SR） in an FitzHugh-Nagumo （FHN） model with an additive LEvy noise numerically. The non-Gaussian LEvy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio （SNR）, and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the LEvy noise and the FHN model on the SR will be exam- ined, and some mechanisms of the LEvy noise-induced SR are presented which are different from those of the Gaussian noise.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172233,11272258,and 11302170)
文摘The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.
基金Project supported by the National Natural Science Foundation of China(Grant No.61371164)the Chongqing Municipal Distinguished Youth Foundation,China(Grant No.CSTC2011jjjq40002)the Research Project of Chongqing Municipal Educational Commission,China(Grant No.KJ130524)
文摘Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.
