scholarly journals Pattern formation in a reaction–diffusion rumor propagation system with Allee effect and time delay

2022 ◽  
Author(s):  
Linhe Zhu ◽  
Le He
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Rumor Propagation

scholarly journals Pattern formation in a reaction-diffusion rumor propagation system with Allee effect and time delay

2021 ◽  
Author(s):  
Linhe Zhu ◽  
Le He
Keyword(s):  
Diffusion Coefficient ◽  
Time Delay ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Small Time ◽  
Diffusion Behavior ◽  
Rumor Propagation ◽  
Reaction Diffusion Model ◽  
Stability And Instability

Abstract This paper analyzes the diffusion behavior of the suspicious and the infected cabins in cyberspace by establishing a rumor propagation reaction diffusion model with Allee effect and time delay. The Turing instability conditions of the system under various conditions are emphatically studied. After considering the delay effect of rumor propagation systems, we have studied the correlation between the stability of the system under the influence of small time delay and the homogeneous system near the equilibrium point, and the critical condition of the delay-induced spatial instability is given. Further considering the possibility of diffusion coefficient changing with time, the critical parameter curves of stability and instability of approximate systems are given by means of Floquet theory, and the necessary conditions of Turing-instability of periodic coefficient are studied. In the numerical simulations, we find that the variation of diffusion coefficient will change the pattern type, and the periodical diffusion behavior will affect the arrangement of the crowd gathering area in the pattern.

scholarly journals Corrigendum to “Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay”

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Hua Liu ◽  
Yong Ye ◽  
Yumei Wei ◽  
Weiyuan Ma ◽  
Ming Ma ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Liu ◽  
Yong Ye ◽  
Yumei Wei ◽  
Weiyuan Ma ◽  
Ming Ma ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Point Of View ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pattern Formations

In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations.

scholarly journals Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Weiming Wang ◽  
Yongli Cai ◽  
Yanuo Zhu ◽  
Zhengguang Guo
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
Model Dynamics ◽  
And Diffusion

We investigate the spatiotemporal dynamics induced by Allee effect in a reaction-diffusion predator-prey model. In the case without Allee effect, there is nonexistence of diffusion-driven instability for the model. And in the case with Allee effect, the positive equilibrium may be unstable under certain conditions. This instability is induced by Allee effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee effect and diffusion controlled pattern formation growth to holes, stripes-holes mixture, stripes, stripes-spots mixture, and spots replication, which shows that the dynamics of the model with Allee effect is not simple, but rich and complex.

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