Competitive spatially distributed population dynamics models: Does diversity in diffusion strategies promote coexistence?

Braverman, Elena; Kamrujjaman, Md.; Korobenko, Lyudmila

doi:10.1016/j.mbs.2015.03.004

Cited by 22 publications

(33 citation statements)

References 33 publications

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“…Some of previously obtained results [2] can readily be extended to the model generalizing (2.2) to the case of two different carrying capacities…”

Section: Discussionmentioning

confidence: 74%

“…For example, in [2,3,10,11,12,13] in the term ∆(u/P ) the dispersal strategy P was usually chosen as P ≡ K guaranteeing that K is a (globally stable) positive solution of the equation. However, if P (x) ≡ K(x)/h(x), where h is any harmonic function on Ω, K is still a solution.…”

Section: Discussionmentioning

confidence: 99%

“…One of the differences is that [17,Propositions 4.3] assumes non-symmetric interaction (growth) type, compared to the symmetric case in the present paper. The results of [17,Propositions 4.3] can be compared to [2], where different carrying capacities for u and v were considered, and also coexistence was observed.…”

Section: Discussionmentioning

confidence: 99%

“…The effect of environment heterogeneity was studied in [15]. The case when a preferred diffusion strategy alleviated a negative effect of less efficient resources exploitation leading to possible coexistence was recently studied in [2]. However, the question how spatial distribution can promote coexistence compared to homogeneous environment got much less attention.…”

Section: Introductionmentioning

confidence: 99%

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Competitive–cooperative models with various diffusion strategies

Braverman¹,

Kamrujjaman²

2016

Computers & Mathematics with Applications

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The paper is concerned with different types of dispersal chosen by competing species. We introduce a model with the diffusion-type term ∇·[a∇ (u/P )] which includes some previously studied systems as special cases, where a positive space-dependent function P can be interpreted as a chosen dispersal strategy. The well-known result that if the first species chooses P proportional to the carrying capacity while the second does not then the first species will bring the second one to extinction, is also valid for this type of dispersal. However, we focus on the case when the ideal free distribution is attained as a combination of the two strategies adopted by the two species. Then there is a globally stable coexistence equilibrium, its uniqueness is justified. If both species choose the same dispersal strategy, non-proportional to the carrying capacity, then the influence of higher diffusion rates is negative, while of higher intrinsic growth rates is positive for survival in a competition.

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“…Some of previously obtained results [2] can readily be extended to the model generalizing (2.2) to the case of two different carrying capacities…”

Section: Discussionmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Competitive–cooperative models with various diffusion strategies

Braverman¹,

Kamrujjaman²

2016

Computers & Mathematics with Applications

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“…For spatially homogeneous environments and regular dispersal, a slower diffuser [17] is a competition winner, if no other differences between competitors exist. If the environment is spatially heterogeneous then the species using knowledge on the carrying capacity of the environment in its dispersal strategy can bring its regularly diffusing competitor to extinction [7,10,12,23]. The ideal free distribution describes the spatial structure when any movement would decrease the population fitness.…”

Section: Introductionmentioning

confidence: 99%

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations

Braverman

Ilmer

2019

Journal of Theoretical Biology

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The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of "close enough" to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion.

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Existence and stability of traveling wavefronts for a three‐species Lotka–Volterra competitive‐cooperative system with nonlocal dispersal

Yang

Zhang

Jian-xin

2023

Math Methods in App Sciences

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The purpose of this work is to investigate the existence and stability of traveling wavefronts for a three-species competitive-cooperative system with nonlocal dispersal. By applying monotone iteration method combining with a pair of suitable super-and sub-solutions, we establish the existence of traveling wavefronts. The nonexistence of traveling wavefronts is obtained by a contradiction argument. Finally, by using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with relatively large speeds are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wavefronts decays exponentially at negative infinity, but in other locations, the initial data can be very large.

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Competitive spatially distributed population dynamics models: Does diversity in diffusion strategies promote coexistence?

Cited by 22 publications

References 33 publications

Competitive–cooperative models with various diffusion strategies

Competitive–cooperative models with various diffusion strategies

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations

Existence and stability of traveling wavefronts for a three‐species Lotka–Volterra competitive‐cooperative system with nonlocal dispersal

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