Global behavior of a reaction-diffusion model with time delay and Dirichlet condition

2021 ◽  
Vol 271 ◽  
pp. 186-215 ◽  
Author(s):  
Chuangxia Huang ◽  
Yanxiang Tan
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Dirichlet Condition ◽  
Global Behavior ◽  
Reaction Diffusion Model

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.

scholarly journals Bifurcation Analysis of Time-Delay Model of Consumer with the Advertising Effect

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 417 ◽  
Author(s):  
Mahmoud A. Abd-Rabo ◽  
Mohammed Zakarya ◽  
Clemente Cesarano ◽  
Shaban Aly
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Delay Model ◽  
Advertising Effect ◽  
Reaction Diffusion Model ◽  
The Stability ◽  
Main Message ◽  
The Impact

Given the economic importance of advertising and product promotions, we have developed a diffusion model to describe the impact of advertising on sales. The main message of this study is to show the effect of advertising diffusion to convert potential buyers into actual customers which may result in persistent alteration in marketing over time. This work is devoted to studying the dynamic behavior of a reaction-diffusion model and its delayed version with the advertising effect. For the non-delay model, it is proven the existence of Hopf bifurcation. Moreover, the stability and direction of bifurcation of periodic solutions are detected. On the other hand, we consider there is a lag for responding of potential buyers to the advertising. Therefore, the time delay τ is deemed as an additional factor in the diffusion model. We have determined the critical values for the delay parameter that yield periodic solutions. Furthermore, the direction and the stability of bifurcating periodic solutions is studied. For supporting the theoretical analysis and demonstrate complex dynamic behaviors, numerical simulations including families of periodic curves are given.

scholarly journals Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

2020 ◽  
Vol 7 ◽  
Author(s):  
Muhammad Jawaz ◽  
Nauman Ahmed ◽  
Dumitru Baleanu ◽  
Muhammad Rafiq ◽  
Muhammad Aziz-ur Rehman
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Positivity Preserving ◽  
Reaction Diffusion Model ◽  
Hiv Aids

scholarly journals On Nonlinear Reaction-Diffusion Model with Time Delay on Hexagonal Lattice

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 758 ◽  
Author(s):  
Vasyl Martsenyuk ◽  
Olga Veselska
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Numerical Study ◽  
Hexagonal Lattice ◽  
Deterministic Chaos ◽  
Reaction Diffusion ◽  
Qualitative Behavior ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Spatial Operator

In the work, a nonlinear reaction-diffusion model in a class of delayed differential equations on the hexagonal lattice is considered. The system includes a spatial operator of diffusion between hexagonal pixels. The main results deal with the qualitative investigation of the model. The conditions of global asymptotic stability, which are based on the Lyapunov function construction, are obtained. An estimate of the upper bound of time delay, which enables stability, is presented. The numerical study is executed with the help of the bifurcation diagram, phase trajectories, and hexagonal tile portraits. It shows the changes in qualitative behavior with respect to the growth of time delay; namely, starting from the stable focus at small delay values, then through Hopf bifurcation to limit cycles, and finally, through period doublings to deterministic chaos.

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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