scholarly journals Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Zhenzhen Wang ◽  
◽  
Tianshou Zhou ◽  
2019 ◽  
Vol 12 (01) ◽  
pp. 1950004
Author(s):  
Jiao Wang ◽  
Zhixian Yu ◽  
Yanling Meng

The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs. nonlocal dispersal. We first prove the existence of invasion traveling waves via using the theory of asymptotic speeds of spread. Then we prove the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces by using the weighted energy and the squeezing technique.


2014 ◽  
Vol 46 (01) ◽  
pp. 217-240
Author(s):  
Yan-Xia Ren ◽  
Ting Yang

In this article we study the parabolic system of equations which is closely related to a multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this system. Provided with some moment conditions, we show the existence, uniqueness, and asymptotic behaviors of such waves with speed greater than or equal to a critical value c̲ and nonexistence of such waves with speed smaller than c̲.


2019 ◽  
Vol 19 (04) ◽  
pp. 1950028
Author(s):  
Zhenzhen Wang ◽  
Zhehao Huang ◽  
Zhengrong Liu

In this paper, traveling wave for a Fisher–KPP equation with stochastic advection and stochastic environmental capacity is investigated. Some conditions are imposed on the reaction rate and noise intensities such that the stochastic transition front exists. Following the results on stochastic transition front, the existence of stochastic traveling waves for the equation is established. Explicit relation between the wave speed and noise attributes including noise intensities and correlation is shown, which can realize the noise effects. It is found that noises reduce the wave speed. In addition, the positive correlation of noises may complement this reduction in a way. But the negative correlation of noises will further aggravate this reduction. There exists a threshold value on the noise correlation making the traveling wave wandering. If the correlation is larger than this threshold value, the wave travels with a forward tendency. Otherwise, the wave travels with a backward tendency. Bifurcations for asymptotic behaviors of the equation induced by the noise intensities and correlation are presented.


2014 ◽  
Vol 46 (1) ◽  
pp. 217-240
Author(s):  
Yan-Xia Ren ◽  
Ting Yang

In this article we study the parabolic system of equations which is closely related to a multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this system. Provided with some moment conditions, we show the existence, uniqueness, and asymptotic behaviors of such waves with speed greater than or equal to a critical value c̲ and nonexistence of such waves with speed smaller than c̲.


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