Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay

Wu, Xin; Ma, Zhaohai; Yuan, Rong

doi:10.11650/tjm/8048

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…Fisher and Kolmogorove made the influential works [7,17]. We know time delay and spatial diffusion are prevalent in the real world, so the reaction diffusion equation with delay has been studied in recent years(see, [4,20,24,12,29,38]).…”

Section: Introductionmentioning

confidence: 99%

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Xue

Liu

2023

Qual. Theory Dyn. Syst.

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In this paper, we consider the multidimensional stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term in n-dimensional space. It is proved that, all planar traveling waves with speed c > c * are exponentially stable in the form of t − n 2 e −ϵτ σt , where constant σ > 0 and ϵ τ = ϵ(τ ) ∈ (0, 1) is a decreasing function for the time delay τ > 0. While, for the planar traveling waves with speed c = c * , we prove that they are algebraically stable in the form of t − n 2 . The Fourier transform plays a crucial role in transforming the competition systems to a linear delayed differential system. We establish the comparison principle and some estimates in weighted spaces L 1 w (R n ) and W 2,1 w (R n ) to obtain the main results.

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Section: Introductionmentioning

confidence: 99%

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Xue

Liu

2023

Qual. Theory Dyn. Syst.

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show abstract

Section: Introductionmentioning

confidence: 99%

Stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term

Xue

Liu

2022

Preprint

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In this paper, we consider the multidimensional stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term in n–dimensional space. It is proved that, all planar traveling waves with speed c > c* are exponentially stable in the form of t−n/2e−ϵτσt, where constant σ > 0 and ϵτ = ϵ(τ ) ∈ (0, 1) is a decreasing function for the time delay τ > 0. While, for the planar traveling waves with speed c = c*, we prove that they are algebraically stable in the form of t−n/2. The Fourier transform plays a crucial role in transforming the competition systems to a linear delayed differential system. We establish the comparison principle and some estimates in weighted spaces L1w(Rn) and Ww2,1(Rn) to obtain the main results.

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Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay

Cited by 2 publications

References 37 publications

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term

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