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 ◽  
Keyword(s):  
Traveling Waves ◽  
Asymptotic Behaviors ◽  
Kpp Equations

Existence and stability of invasion traveling waves for a competition system with random vs. nonlocal dispersals

2019 ◽  
Vol 12 (01) ◽  
pp. 1950004
Author(s):  
Jiao Wang ◽  
Zhixian Yu ◽  
Yanling Meng
Keyword(s):  
Traveling Waves ◽  
Weighted Spaces ◽  
Nonlocal Dispersal ◽  
Asymptotic Behaviors ◽  
Competition System ◽  
Weighted Energy ◽  
Existence And Stability ◽  
Exponentially Stable ◽  
Exponentially Weighted

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.

scholarly journals Multitype Branching Brownian Motion and Traveling Waves

2014 ◽  
Vol 46 (01) ◽  
pp. 217-240
Author(s):  
Yan-Xia Ren ◽  
Ting Yang
Keyword(s):  
Brownian Motion ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Critical Value ◽  
System Of Equations ◽  
Moment Conditions ◽  
Asymptotic Behaviors ◽  
Branching Brownian Motion ◽  
Parabolic System Of Equations

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.

Stochastic traveling waves of a stochastic Fisher–KPP equation and bifurcations for asymptotic behaviors

2019 ◽  
Vol 19 (04) ◽  
pp. 1950028
Author(s):  
Zhenzhen Wang ◽  
Zhehao Huang ◽  
Zhengrong Liu
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Wave Speed ◽  
Threshold Value ◽  
Environmental Capacity ◽  
Kpp Equation ◽  
Asymptotic Behaviors ◽  
Transition Front ◽  
Stochastic Transition ◽  
Explicit Relation

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.

Multitype Branching Brownian Motion and Traveling Waves

2014 ◽  
Vol 46 (1) ◽  
pp. 217-240
Author(s):  
Yan-Xia Ren ◽  
Ting Yang
Keyword(s):  
Brownian Motion ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Critical Value ◽  
System Of Equations ◽  
Moment Conditions ◽  
Asymptotic Behaviors ◽  
Branching Brownian Motion ◽  
Parabolic System Of Equations

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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