scholarly journals Global Stability of a Lotka-Volterra Competition-Diffusion-Advection System with Different Positive Diffusion Distributions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 166
Author(s):  
Lili Chen ◽  
Shilei Lin ◽  
Yanfeng Zhao
Keyword(s):  
Global Stability ◽  
Stability Result ◽  
Functional Method ◽  
Heterogeneous Environments ◽  
Homogeneous Steady State ◽  
Competition Ability ◽  
Lyapunov Functional Method ◽  
And Diffusion ◽  
Biological Organisms ◽  
Competition Diffusion

In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.

Global stability for a multi-group SVIR model with age of vaccination

2018 ◽  
Vol 11 (05) ◽  
pp. 1850068 ◽  
Author(s):  
Chuncheng Wang ◽  
Dejun Fan ◽  
Ling Xia ◽  
Xiaoyu Yi
Keyword(s):  
Global Stability ◽  
Functional Method ◽  
Theoretic Approach ◽  
Connected Component ◽  
Protective Properties ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Reproduction Numbers ◽  
Strongly Connected ◽  
Lyapunov Functional Method

In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investigated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.

scholarly journals Global Directed Dynamic Behaviors of a Lotka-Volterra Competition-Diffusion-Advection System

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 195
Author(s):  
Lili Chen ◽  
Shilei Lin ◽  
Yanfeng Zhao
Keyword(s):  
Dynamical System ◽  
Principal Eigenvalue ◽  
Dynamical System Theory ◽  
Heterogeneous Environments ◽  
Dynamic Behaviors ◽  
Dynamical Behaviors ◽  
Further Development ◽  
And Diffusion ◽  
Competition Diffusion

This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments. The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards a positive distribution. By virtue of the principal eigenvalue theory, the linear stability of the co-existing steady state is established. Furthermore, the classification of dynamical behaviors is shown by utilizing the monotone dynamical system theory. This work can be seen as a further development of a competition-diffusion system.

Global stability result for parabolic Cauchy problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mourad Choulli ◽  
Masahiro Yamamoto
Keyword(s):  
New York ◽  
Partial Differential Equations ◽  
Global Stability ◽  
Classical Problem ◽  
Stability Result ◽  
Cauchy Problems ◽  
Smooth Solutions ◽  
Linear Partial Differential Equations ◽  
Ill Posed ◽  
The Stability

AbstractUniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953], these kind of problems are known to be ill-posed and even severely ill-posed. Until now, there are only few partial results concerning the quantification of the stability of parabolic Cauchy problems. We bring in the present work an answer to this issue for smooth solutions under the minimal condition that the domain is Lipschitz.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

scholarly journals Global Exponential Stability of Learning-Based Fuzzy Networks on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Juan Chen ◽  
Zhenkun Huang ◽  
Jinxiang Cai
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Fuzzy Neural Networks ◽  
New Learning ◽  
Fuzzy Neural ◽  
Lyapunov Functional Method

We investigate a class of fuzzy neural networks with Hebbian-type unsupervised learning on time scales. By using Lyapunov functional method, some new sufficient conditions are derived to ensure learning dynamics and exponential stability of fuzzy networks on time scales. Our results are general and can include continuous-time learning-based fuzzy networks and corresponding discrete-time analogues. Moreover, our results reveal some new learning behavior of fuzzy synapses on time scales which are seldom discussed in the literature.

A Result in Artificial Intelligence

2010 ◽  
Vol 439-440 ◽  
pp. 1549-1554
Author(s):  
Jie Min Zhao
Keyword(s):  
Artificial Intelligence ◽  
Time Delay ◽  
Global Stability ◽  
Finite Time ◽  
Stability Result ◽  
Liapunov Functional ◽  
Computing Method

Consider a class of artificial intelligence model with finite time–delay. We construct a Liapunov functional. A global stability result is given by means of the analysis and computing method.

The evolution of slender inviscid drops in an axisymmetric straining flow

1980 ◽  
Vol 101 (3) ◽  
pp. 545-553 ◽  
Author(s):  
E. J. Hinch
Keyword(s):  
Global Stability ◽  
Stable Equilibrium ◽  
Stability Result ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Initial Shape ◽  
Low Reynolds Numbers ◽  
Long Wavelength ◽  
Shape Equation ◽  
Low Reynolds

The evolution of the shape of a slender inviscid drop in an axisymmetric straining motion is studied at low Reynolds numbers. It is found that the shape equation can be solved by polynommals with time-dependent coefficients. A global stability result can be used to show simply that only one possible equilibrium is stable. It is further shown that if the slender drop starts with a long-wavelength waist then it cannot go to this stable equilibrium and must either extend indefinitely or burst. In the class of trinomial shapes, it is shown that the drop either bursts or goes to the stable equilibrium, depending on whether or not the initial shape has a waist.

scholarly journals Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Haiyong Zheng ◽  
Bin Wu ◽  
Tengda Wei ◽  
Linshan Wang ◽  
Yangfan Wang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Differential Inequality ◽  
Time Delays ◽  
Functional Method ◽  
High Order ◽  
Distributed Time Delays ◽  
Inequality Technique ◽  
Global Exponential Robust Stability ◽  
Lyapunov Functional Method

By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

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