On the stability of a “reaction-diffusion” model in ecological systems

1978 ◽  
Vol 98 (6) ◽  
pp. 121-126
Author(s):  
Koichi Harada ◽  
Takeshi Fukao
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Ecological Systems ◽  
Reaction Diffusion Model ◽  
The Stability

scholarly journals Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1516
Author(s):  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Stelios Bekiros ◽  
Jinping Liu ◽  
Hadi Jahanshahi ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Linear Control ◽  
Control Law ◽  
Synchronization Problem ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions ◽  
Error System ◽  
The Stability ◽  
Complex Formations

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions.

scholarly journals The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime

2014 ◽  
Vol 19 (5) ◽  
pp. 1373-1410 ◽  
Author(s):  
Theodore Kolokolnikov ◽  
◽  
Michael J. Ward ◽  
Juncheng Wei ◽  
◽  
...  
Keyword(s):  
Steady State ◽  
Diffusion Model ◽  
Hot Spot ◽  
Reaction Diffusion ◽  
Urban Crime ◽  
Reaction Diffusion Model ◽  
The Stability

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 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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