Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments

2021 ◽  
Vol 153 ◽  
pp. 111542
Author(s):  
Junlang Hu ◽  
Linhe Zhu
Keyword(s):  
Time Delay ◽  
Pattern Analysis ◽  
Reaction Diffusion ◽  
Turing Pattern ◽  
Rumor Propagation ◽  
System With Time Delay ◽  
Network Environments

Stability and Hopf Bifurcation of a Reaction–Diffusion Neutral Neuron System with Time Delay

2017 ◽  
Vol 27 (14) ◽  
pp. 1750214 ◽  
Author(s):  
Tao Dong ◽  
Linmao Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neuron System ◽  
Center Manifold Theorem ◽  
Feedback Strength ◽  
The Stability ◽  
System With Time Delay ◽  
Zero Equilibrium

In this paper, a type of reaction–diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.

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 Trajectory Tracking Control for Reaction–Diffusion System with Time Delay Using P-Type Iterative Learning Method

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 186
Author(s):  
Yaqiang Liu ◽  
Jianzhong Li ◽  
Zengwang Jin
Keyword(s):  
Time Delay ◽  
Tracking Control ◽  
Reaction Diffusion ◽  
Delay System ◽  
Distribution Functions ◽  
Iterative Learning ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Trajectory Tracking Control ◽  
System With Time Delay

This paper has dealt with a tracking control problem for a class of unstable reaction–diffusion system with time delay. Iterative learning algorithms are introduced to make the infinite-dimensional repetitive motion system track the desired trajectory. A new Lyapunov–Krasovskii functional is constructed to deal with the time-delay system. Picewise distribution functions are applied in this paper to perform piecewise control operations. By using Poincaré–Wirtinger inequality, Cauchy–Schwartz inequality for integrals and Young’s inequality, the convergence of the system with time delay using iterative learning schemes is proved. Numerical simulation results have verified the effectiveness of the proposed method.

Pattern dynamics of a diffusive predator–prey model with delay effect

2017 ◽  
Vol 10 (04) ◽  
pp. 1750059 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Dongliang Li
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Reaction Diffusion ◽  
Wave Pattern ◽  
Turing Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pattern Dynamics ◽  
Predator Prey Models ◽  
Parameter Values

We study the spatiotemporal dynamics in a diffusive predator–prey system with time delay. By investigating the dynamical behavior of the system in the presence of Turing–Hopf bifurcations, we present a classification of the pattern dynamics based on the dispersion relation for the two unstable modes. More specifically, we researched the existence of the Turing pattern when control parameters lie in the Turing space. Particularly, when parameter values are taken in Turing–Hopf domain, we numerically investigate the formation of all the possible patterns, including time-dependent wave pattern, persistent short-term competing dynamics and stationary Turing pattern. Furthermore, the effect of time delay on the formation of spatial pattern has also been analyzed from the aspects of theory and numerical simulation. We speculate that the interaction of spatial and temporal instabilities in the reaction–diffusion system might bring some insight to the finding of patterns in spatial predator–prey models.

Design of Master's Position Controller for Bilateral Control System with Time Delay

2015 ◽  
Vol 135 (3) ◽  
pp. 268-275 ◽  
Author(s):  
Daisuke Yashiro ◽  
Tadashi Hieno ◽  
Kazuhiro Yubai ◽  
Satoshi Komada
Keyword(s):  
Control System ◽  
Time Delay ◽  
Bilateral Control ◽  
Position Controller ◽  
System With Time Delay

scholarly journals A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Parameter Identification ◽  
Typical Feature ◽  
The Novel ◽  
Isolation Rate ◽  
High Isolation ◽  
The Government ◽  
System With Time Delay ◽  
Official Data

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

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