Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

Hsu, Cheng-Hsiung; Yang, Tsung-Ying; Yu, Zhixian

doi:10.1088/1361-6544/aa99a1

Cited by 21 publications

(14 citation statements)

References 35 publications

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“…At present, the traveling waves for autonomous reaction-diffusion and nonlocal diffusion epidemic models have been studied extensively. Some important results can be found in the literatures [7] , [8] , [9] , [10] , [13] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] and their references.…”

Section: Introductionmentioning

confidence: 95%

The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

Teng

2021

Chaos, Solitons & Fractals

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In this paper, a reaction-diffusion SIR epidemic model is proposed. It takes into account the individuals mobility, the time periodicity of the infection rate and recovery rate, and the general nonlinear incidence function, which contains a number of classical incidence functions. In our model, due to the introduction of the general nonlinear incidence function, the boundedness of the infected individuals can not be obtained, so we study the existence and nonexistence of periodic traveling wave solutions of original system with the aid of auxiliary system. The basic reproduction number and the critical wave speed are given. We obtained the existence and uniqueness of periodic traveling waves for each wave speed using the Schauder’s fixed points theorem when . The nonexistence of periodic traveling waves for two cases (i) and (ii) and are also obtained. These results generalize and improve the existing conclusions. Finally, the numerical experiments support the theoretical results. The differences of traveling wave solution between periodic system and general aperiodic coefficient system are analyzed by numerical simulations.

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Section: Introductionmentioning

confidence: 95%

The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

Teng

2021

Chaos, Solitons & Fractals

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“…For system (1.6), Hsu and Yang [21] investigated the existence, uniqueness and asymptotic behavior of traveling waves for (1.6). More recently, using the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, the techniques of weighted energy method and comparison principle, Hsu et al [22] extended (1.6) to more general delayed systems and obtained the existence and stability of traveling waves. For the lattice system (1.4), Guo and Wu [15,16] recently investigated the existence of entire solutions and traveling wave fronts and its properties for the two-component spatially discrete competitive system…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it is significant to see whether the traveling wave solutions are stable or not. Motivated by [16,21,22], we will investigate the existence and stability of traveling wave fronts of system (1.3).…”

Section: Introductionmentioning

confidence: 99%

Wave propagation and its stability for a class of discrete diffusion systems

Yu,

Wan,

Hsu

2019

Preprint

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This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the techniques of weighted energy method and the comparison principle, we show that all solutions of the Cauchy problem for the discrete diffusive systems converge exponentially to the traveling wave fronts when the initial perturbations around the wave fronts lie in a suitable weighted Sobolev space. Our main results can be extended to more general discrete diffusive systems. We also apply them to the discrete epidemic model with the Holling-II type and Richer type effects.

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“…The existence and stability of traveling waves of (4) have been extensively studied, see [7,19,21,24] and references therein. Note that system (1) is also a delay version of the following system…”

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confidence: 99%

“…In fact, by [8, Lemma 2.1], we can differentiate the series on t variable in (9). Using the recurrence relation (7), we obtain…”

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confidence: 99%

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

Liu

Zhang

2021

era

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This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. Using the Fourier transform and the weighted energy method with a suitably selected weighted function, we prove that the monotone or non-monotone traveling waves are exponentially stable in L ∞ (R) × L ∞ (R) with the exponential convergence rate e −µt for some constant µ > 0.

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Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

Cited by 21 publications

References 35 publications

The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

Wave propagation and its stability for a class of discrete diffusion systems

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

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