Spatial Dynamics of a Nonlocal Periodic Reaction-Diffusion Model with Stage Structure

2009 ◽  
Vol 40 (6) ◽  
pp. 2496-2516 ◽  
Author(s):  
Yu Jin ◽  
Xiao-Qiang Zhao
Keyword(s):  
Diffusion Model ◽  
Spatial Dynamics ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Reaction Diffusion Model ◽  
Periodic Reaction

scholarly journals TRAVELING WAVE SOLUTIONS IN A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL WITH ADVECTION

2015 ◽  
Vol 20 (2) ◽  
pp. 168-187
Author(s):  
Liang Zhang ◽  
Huiyan Zhao
Keyword(s):  
Diffusion Model ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Delayed Reaction ◽  
Wave Solutions ◽  
Reaction Diffusion Model ◽  
Travelling Fronts ◽  
Appl Math

We investigate a stage-structured delayed reaction-diffusion model with advection that describes competition between two mature species in water flow. Time delays are incorporated to measure the time lengths from birth to maturity of the populations. We show there exists a finite positive number c∗ that can be characterized as the slowest spreading speed of traveling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. The model and mathematical result in [J.F.M. Al-Omari, S.A. Gourley, Stability and travelling fronts in Lotka–Volterra competition models with stage structure, SIAM J. Appl. Math. 63 (2003) 2063–2086] are generalized.

scholarly journals Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ning Wang ◽  
Zhi-Cheng Wang
Keyword(s):  
Diffusion Model ◽  
Critical Speed ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Reaction Diffusion ◽  
Linear Operators ◽  
Time Space ◽  
Reaction Diffusion Model ◽  
Periodic Reaction ◽  
Asymptotic Speed

<p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.</p>

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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