On a second order eigenvalue problem and its application

Yuan, Shao; Wang, Jinbao; Zhou, Peng

doi:10.1016/j.jde.2022.04.030

Cited by 14 publications

(3 citation statements)

References 30 publications

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“…It seems like that the role of spatial heterogeneity in advection rate is less studied. To our best knowledge, the only such work on reaction-diffusion-advection competition models for stream species is by Shao et al [34], which shows that the slower diffuser may win if the advection rate function is concave.…”

Section: Introductionmentioning

confidence: 99%

Evolution of dispersal in advective patchy environments with varying drift rates

Chen¹,

Liu²,

Wu³

2023

Preprint

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In this paper, we study a two stream species Lotka-Volterra competition patch model with the patches aligned along a line. The two species are supposed to be identical except for the diffusion rates. For each species, the diffusion rates between patches are the same, while the drift rates vary. Our results show that the convexity of the drift rates has a significant impact on the competition outcomes: if the drift rates are convex, then the species with larger diffusion rate wins the competition; if the drift rates are concave, then the species with smaller diffusion rate wins the competition.

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Section: Introductionmentioning

confidence: 99%

Evolution of dispersal in advective patchy environments with varying drift rates

Chen¹,

Liu²,

Wu³

2023

Preprint

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“…In fact, many researchers have constructed reaction-diffusion-advection systems to study the dynamics of species in advective environments [16,20,24,32,36,37,39,41,44,45,48,54,26]. How individuals prevent flow-induced washout and persist in advective environments has puzzled ecologists for decades.…”

mentioning

confidence: 99%

“…There are a lot of interesting problems deserving further investigation. The advection speed and other biological parameters may differ at different locations [37]. How does the advection rate alter the dynamics of the system in spatially heterogeneous environments?…”

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confidence: 99%

Disease transmission dynamics of an epidemiological predator-prey system in open advective environments

Yuan

Wang

2023

DCDS-B

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<p style='text-indent:20px;'>This paper delves into the dynamics of a spatial eco-epidemiological system with disease spread within the predator population in open advective environments. The disease-free subsystem is first discussed, and the net reproductive rate <inline-formula><tex-math id="M1">\begin{document}$ R_P $\end{document}</tex-math></inline-formula> is established to determine whether the predator can invade successfully. The impacts of advection rate on <inline-formula><tex-math id="M2">\begin{document}$ R_P $\end{document}</tex-math></inline-formula> are also discussed. Then for the scenario of successful invasion of the predator, sufficient conditions for the prevalence of disease and the local stability of disease-free attractor are obtained by dint of persistence theory and comparison theorem. Finally, we present a special numerical example, in which the basic reproduction ratio <inline-formula><tex-math id="M3">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> of the disease is established in the absence or presence of periodic perturbation. Our theoretical and numerical results both indicate that the advection rate in an intermediate interval can favor the coexistence of prey and healthy predator as well as the eradication of disease.</p>

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A Time-Periodic Parabolic Eigenvalue Problem on Finite Networks and Its Applications

Jin,

Peng

2024

J Nonlinear Sci

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On a second order eigenvalue problem and its application

Cited by 14 publications

References 30 publications

Evolution of dispersal in advective patchy environments with varying drift rates

Evolution of dispersal in advective patchy environments with varying drift rates

Disease transmission dynamics of an epidemiological predator-prey system in open advective environments

A Time-Periodic Parabolic Eigenvalue Problem on Finite Networks and Its Applications

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