Numerical Dynamics of Integrodifference Equations: Global Attractivity in a $C^0$-Setting

2019 ◽  
Vol 57 (5) ◽  
pp. 2121-2141
Author(s):  
Christian Poetzsche
Keyword(s):  
Global Attractivity ◽  
Integrodifference Equations ◽  
Numerical Dynamics

Dynamics of an infection age-space structured cholera model with Neumann boundary condition

2021 ◽  
pp. 1-30
Author(s):  
WEIWEI LIU ◽  
JINLIANG WANG ◽  
RAN ZHANG
Keyword(s):  
Vibrio Cholerae ◽  
Disease Transmission ◽  
Global Attractivity ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Human Populations ◽  
Global Dynamics ◽  
Infection Age ◽  
Reaction Diffusion Model ◽  
Disease Persistence

This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝ n . We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

scholarly journals Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

2017 ◽  
Vol 62 (10) ◽  
pp. 4905-4916 ◽  
Author(s):  
Nikita Barabanov ◽  
Johannes Schiffer ◽  
Romeo Ortega ◽  
Denis Efimov
Keyword(s):  
Global Attractivity ◽  
Synchronous Generator

scholarly journals Permanence and Global Attractivity of a Discrete Two-Prey One-Predator Model with Infinite Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Zhixiang Yu ◽  
Zhong Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Predator Model

A discrete two-prey one-predator model with infinite delay is proposed. A set of sufficient conditions which guarantee the permanence of the system is obtained. By constructing a suitable Lyapunov functional, we also obtain sufficient conditions ensuring the global attractivity of the system. An example together with its numerical simulation shows the feasibility of the main results.

On the global attractivity and the periodic character of some difference equations

2001 ◽  
Vol 7 (6) ◽  
pp. 837-850 ◽  
Author(s):  
H. El—metwallya ◽  
E. A Grove ◽  
G. Ladas ◽  
H.D. Voulov
Keyword(s):  
Difference Equations ◽  
Global Attractivity
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