Dynamics of a three species competition model

Lou, Yuan; Munther, Daniel

doi:10.3934/dcds.2012.32.3099

Cited by 32 publications

(27 citation statements)

References 15 publications

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“…, q = 1 gives us the following uniform bound (35) ||∇u t || 2 2 ≤ C, t > T 7 = T 6 + 1 Similar methods applied to the equation for v and r yield…”

Section: Long Time Dynamicsmentioning

confidence: 95%

“…We aim to show the convergence of both the right hand side strongly in L 2 . Due to the uniform bounds via (30), (35), (33) and the embedding of H 1 (Ω) → L 4 (Ω) → L 2 (Ω) and H 2 (Ω) → L ∞ (Ω) we obtain a subsequence u nj stil labeled u n s.t…”

Section: Long Time Dynamicsmentioning

confidence: 99%

“…[54] Therefore understanding and subsequently attenuating the spread of invasive species is an important and practical problem in spatial ecology and much work has been devoted to this issue [1,4,10,38,40,53]. More recently, the spread of natural and invasive species by nonrandom dispersal, say due to competitive pressures, is of great interest [2,35]. However, there has been less focus, on the actual eradication of an invasive species, once it has already invaded.…”

Section: Introductionmentioning

confidence: 99%

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Biological control via “ecological” damping: An approach that attenuates non-target effects

Parshad

Quansah

Black

et al. 2016

Mathematical Biosciences

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Abstract. In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blowup in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous" levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in [43]. Lastly, we confirm the existence of spatio-temporal chaos.

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“…, q = 1 gives us the following uniform bound (35) ||∇u t || 2 2 ≤ C, t > T 7 = T 6 + 1 Similar methods applied to the equation for v and r yield…”

Section: Long Time Dynamicsmentioning

confidence: 95%

Section: Long Time Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Biological control via “ecological” damping: An approach that attenuates non-target effects

Parshad

Quansah

Black

et al. 2016

Mathematical Biosciences

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“…The case of three species for a particular diffusion strategy was considered in [14]. It would be interesting to incorporate the approach of the present paper to dispersal with consideration of more than two (and probably three) competing species, as well as patchy environment [8].…”

Section: Discussionmentioning

confidence: 99%

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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“…The detrimental effects of aquatic invasive species is well-documented [3,4,5,6,17,19,21,30,33]. Subsequently, a tremendous amount of effort by habitat controllers is devoted to designing effective eradication strategies such as chemical treatment, local harvesting, dewatering, ichthyocides, or a suitable combination [29].…”

Section: Introductionmentioning

confidence: 99%

Optimal control and analysis of a modified trojan Y-Chromosome strategy

Beauregard

Parshad

Boon

et al. 2020

Ecological Modelling

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The Trojan Y Chromosome (TYC) Strategy is a promising eradication method that attempts to manipulate the female to male ratio to promote the reduction of the population of an invasive species. The manipulation stems from an introduction of sex-reversed males, called supermales, into an ecosystem. The offspring of the supermales is guaranteed to be male. Mathematical models have shown that the population can be driven to extinction with a continuous supply of supermales. In this paper, a new model of the TYC strategy is introduced and analyzed that includes two important modeling characteristics, that are neglected in all previous models. First, the new model includes intraspecies competition for mates. Second, a strong Allee effect is included. Several conclusions about the strategy via optimal control are established. These results have large scale implications for the biological control of invasive species.

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Dynamics of a three species competition model

Cited by 32 publications

References 15 publications

Biological control via “ecological” damping: An approach that attenuates non-target effects

Biological control via “ecological” damping: An approach that attenuates non-target effects

Competitive–cooperative models with various diffusion strategies

Optimal control and analysis of a modified trojan Y-Chromosome strategy

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