TRAVELING WAVES FOR A SIRS MODEL WITH NONLOCAL DIFFUSION

2012 ◽  
Vol 05 (05) ◽  
pp. 1250036 ◽  
Author(s):  
XIAOJING YU ◽  
CHUFEN WU ◽  
PEIXUAN WENG
Keyword(s):  
Traveling Waves ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Iteration Scheme ◽  
Lower Solution ◽  
Nonlocal Diffusion ◽  
Well Posedness ◽  
Upper Solution ◽  
Sirs Model ◽  
Two Equilibria

In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.

scholarly journals Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Solitary Wave ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Periodic Wave ◽  
Point Of View ◽  
Bifurcation Method ◽  
Wave Solutions

The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.

scholarly journals Speed determinacy of the traveling waves for a three species time-periodic Lotka-Volterra competition system

2021 ◽  
Author(s):  
Qiong Wu ◽  
Chaohong Pan ◽  
Hongyong Wang
Keyword(s):  
Traveling Waves ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Competition System ◽  
Periodic Traveling Waves ◽  
Minimal Wave Speed ◽  
Speed Selection ◽  
Time Periodic ◽  
Selection Of

In this paper, speed selection of the time periodic traveling waves for a three species time-periodic Lotka-Volterra competition system is studied via the upper-lower solution method as well as the comparison principle. Through constructing specific types of upper and lower solutions to the system, the speed selection of the minimal wave speed can be determined under some sets of sufficient conditions composed of the parameters in the system.

Traveling wave solutions in n-dimensional delayed nonlocal diffusion system with mixed quasimonotonicity

2014 ◽  
Vol 13 (01) ◽  
pp. 23-43
Author(s):  
Weifang Yan ◽  
Rui Liu
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Iteration Scheme ◽  
Existence Results ◽  
Nonlocal Diffusion ◽  
Volterra Model ◽  
Wave Solutions ◽  
Delayed System ◽  
Definition Of ◽  
Special Case

This paper is devoted to the study of an n-dimensional delayed system with nonlocal diffusion and mixed quasimonotonicity. By developing a new definition of upper–lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. These results are applied to a nonlocal diffusion model which takes the four-species Lotka–Volterra model as its special case.

TRAVELING WAVES IN A REACTION-DIFFUSION PREDATOR-PREY SYSTEM WITH NONLOCAL DELAYS

2012 ◽  
Vol 05 (05) ◽  
pp. 1250043
Author(s):  
ZHE LI ◽  
RUI XU
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Iteration Scheme ◽  
Monotonicity Condition ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Theoretical Results

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with nonlocal delays. By introducing a partially exponential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.

scholarly journals Traveling Waves in the Underdamped Frenkel–Kontorova Model

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hengyan Li ◽  
Shaowei Liu
Keyword(s):  
Boundary Condition ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Traveling Wave Solutions ◽  
Iteration Scheme ◽  
Moser Iteration ◽  
Wave Solutions ◽  
Kontorova Model

This paper studies a damped Frenkel–Kontorova model with periodic boundary condition. By using Nash–Moser iteration scheme, we prove that such model has a family of smooth traveling wave solutions.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

Dynamic behavior of a stochastic SIRS model with two viruses

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang ◽  
Zhixia Han
Keyword(s):  
Growth Rate ◽  
Asymptotic Stability ◽  
Global Existence ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Sirs Model ◽  
The Moment ◽  
Disease Free

AbstractTo study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically ultimately bounded and the moment average in time of the positive solution is bounded. Our results mean that the environmental noise suppresses the growth rate of the individuals and drives the disease to extinction under certain conditions. Finally, numerical simulations are given to illustrate our main results.

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