scholarly journals Bifurcation phenomena in a single-species reaction-diffusion model with spatiotemporal delay

2021 ◽  
Vol 6 (7) ◽  
pp. 6687-6698
Author(s):  
Gaoxiang Yang ◽  
◽  
Xiaoyu Li ◽  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Single Species ◽  
Bifurcation Phenomena ◽  
Reaction Diffusion Model ◽  
Spatiotemporal Delay

Effect of delay on pattern formation of a Rosenzweig–MacArthur type reaction–diffusion model with spatiotemporal delay

2021 ◽  
Author(s):  
Gao-Xiang Yang ◽  
Xiao-Yu Li
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Multiple Scale ◽  
Predator Prey ◽  
Turing Bifurcation ◽  
Reaction Diffusion Model ◽  
Scale Perturbation ◽  
Spatiotemporal Delay ◽  
Theoretical Results

In this paper, a predator–prey reaction–diffusion model with Rosenzweig–MacArthur type functional response and spatiotemporal delay is investigated through using the tool of Turing bifurcation theories. First, by taking the average time delay as a bifurcation parameter, conditions of occurrence of Turing bifurcation are obtained through employing the Routh–Hurwitz criteria. Second, as the average time delay varies the amplitude equations of Turing bifurcation patterns including spots pattern and stripes pattern are also obtained through the multiple scale perturbation method. Finally, the two kinds of spatiotemporal evolution distributions of species such as spots pattern and stripes pattern are shown to illustrate theoretical results.

Pattern dynamics of a predator–prey reaction–diffusion model with spatiotemporal delay

2015 ◽  
Vol 81 (4) ◽  
pp. 2155-2163 ◽  
Author(s):  
Jian Xu ◽  
Gaoxiang Yang ◽  
Hongguang Xi ◽  
Jianzhong Su
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Predator Prey ◽  
Pattern Dynamics ◽  
Reaction Diffusion Model ◽  
Spatiotemporal Delay

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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