scholarly journals Global stability of traveling waves for a spatially discrete diffusion system with time delay

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Ting Liu ◽  
◽  
Guo-Bao Zhang
Keyword(s):  
Time Delay ◽  
Global Stability ◽  
Traveling Waves ◽  
Diffusion System ◽  
System With Time Delay

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.

Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka–Volterra System with Time Delay

2015 ◽  
Vol 25 (06) ◽  
pp. 1550089
Author(s):  
Xiaoyuan Chang ◽  
Junjie Wei
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Three Dimensional ◽  
Steady State Solution ◽  
State Solution ◽  
Diffusion System ◽  
Asymptotic Expressions ◽  
The Stability ◽  
System With Time Delay

In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka–Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka–Volterra diffusion system with time delay to illustrate our conclusions.

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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