Effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model

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.

Analysis of weak signal detection based on tri-stable system under Levy noise

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.

AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LéVY NOISE

In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.

Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps

A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.

Lévy noise induced stochastic resonance in an FHN model

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.

Well-posedness for the stochastic 2D primitive equations with Lévy noise

The two-dimensional primitive equations with Lévy noise are studied in this paper.We prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak convergence method and monotonicity arguments.

Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

Environmental perturbations are unavoidable in the propagation of infectious diseases.In this paper,we introduce the stochasticity into the susceptible-infected recovered(SIR)model via thc^parameter perturbation method.The stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations:Gaussian white noise and Levy jumps,respectively.This idea provides an overview of disease dynamics under different random perturbation scenarios.By using new techniques and methods,we study certain interesting asymptotic properties of our perturbed model,namely:persistence in the mean,ergodicity and extinction of the disease.For illustrative purposes,numerical examples are presented for checking the theoretical study.

Analysis on stochastic dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered.We first show the existence of the global positive solution,then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species.In the meanwhile,numerical simulations are carried to support results.Finally,we show the existence of the stationary distribution for a special case.

Dynamic of a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments

This paper is concerned with a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments.First,under some simple assumptions,we prove that there exists a unique global nonnegative solution which is permanent in time average.Moreover,sufficient criteria for the extinction of each species are obtained.Finally,we carry out some numerical simulations to verify the theoretical results.