Movement, competition and pattern formation in a two prey–one predator food chain model

Djomegni, P.M. Tchepmo; Govinder, K. S.; Goufo, Emile Franc Doungmo

doi:10.1007/s40314-017-0459-4

Cited by 10 publications

(2 citation statements)

References 44 publications

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“…Kara and Batabyal () considered different Holing type response for each group of prey. Tchepmo Djomegni, Govinder, and Doungmo Goufo () used a threshold quantity to analyze their competition model. Moreover, they introduced the average velocity of animals and investigated the impact of movement on the overall dynamics of the system.…”

Section: Harvesting Modelmentioning

confidence: 99%

Coexistence and harvesting control policy in a food chain model with mutual defense of prey

Djomegni

Goufo

Sahu

et al. 2019

Natural Resource Modeling

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A model is proposed to understand the dynamics in a food chain (one predator‐two prey). Unlike many approaches, we consider mutualism (for defense against predators) between the two groups of prey. We investigate the conditions for coexistence and exclusion. Unlike Elettreby's (2009) results, we show that prey can coexist in the absence of predators (as expected since there is no competition between prey). We also show the existence of Hopf bifurcation and limit cycle in the model, and numerically present bifurcation diagrams in terms of mutualism and harvesting. When the harvest is practiced for profit making, we provide the threshold effort value ξ0 that determines the profitability of the harvest. We show that there is zero profit when the constant effort ξ0 is applied. Below (resp. above) ξ0, there will always be gain (resp. loss). In the case of gain, we provide the optimal effort ξ* and optimal steady states that produce maximum profit and ensure coexistence. Recommendations for resource managers As a result of our investigation, we bring the following to the attention of management: In the absence of predators, different groups of prey can coexist if they mutually help each other (no competition among them). There is a maximal effort ξ0 to invest in order to gain profit from the harvest. Above ξ0, the investment will result in a loss. In the case of profit from harvest, policy makers should recommend the optimal effort ξ* to be applied and the optimal stock (x1*,x2*,y*) to harvest. This will guarantee maximum profit while ensuring sustainability of all species.

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Section: Harvesting Modelmentioning

confidence: 99%

Coexistence and harvesting control policy in a food chain model with mutual defense of prey

Djomegni

Goufo

Sahu

et al. 2019

Natural Resource Modeling

Self Cite

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“…Some examples of this directed movement can be found in living species in rivers, lakes, and oceans, as well as in marine species along coastlines. Various advection models have been formulated in order to highlight the possible different types of taxis, with or without the additional presence of random dispersion (e.g., [17][18][19][20][21][22][23][24] and the references therein). It has been observed (e.g., [25]) that often animals move aggregated in groups or bands.…”

Section: Introductionmentioning

confidence: 99%

Traveling Band Solutions in a System Modeling Hunting Cooperation

Carfora

Torcicollo

2022

Mathematics

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A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. In order to examine the band behavior of species over time, traveling wave solutions were introduced, and conditions for the coexistence of both populations and/or extinction were found. Numerical simulations illustrating the obtained results were performed.

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