Mathematical Model of the Dynamics of Fish, Waterbirds and Tourists in the Djoudj National Park, Senegal

Diop, Oumar; Sène, Abdou

doi:10.1007/s10441-016-9290-3

Cited by 2 publications

(1 citation statement)

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“…Casagrandi and Rinaldi's model was likely one of the first works that related the notion of sustainability with structural properties of stable equilibria points. From the dynamical systems perspective, other authors have analyzed how the forest resources and the wildlife are affected by the tourists (Afsharnezhad & Monfared, 2017; Behjaty & Monfared, 2019; Casagrandi & Rinaldi, 2004; Diop & Sène, 2016, 2018; Kaslik & Neamtu, 2020; Lacitignola et al, 2007; Monfared et al, 2016). Through these models, it can be concluded that these socioecological systems might present sustainable scenarios of the coexistence of tourists and nature.…”

Section: Introductionmentioning

confidence: 99%

Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

Villavicencio-Pulido

Vázquez–Hipólito

García‐Cruz

2022

Natural Resource Modeling

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In this work, we propose a socioecological model to describe the effects of visiting tourists in biological attractive sites. We model conditioned interactions between the forest resources and the wildlife with the tourists. This allows us to describe the net benefits-costs rates that the species and their habitats receive from the interaction with tourists. We show that when a scenario of sustainable tourism exists, it is always at risk. This occurs because there is at least a component of the socioecological system that can go to zero when the initial conditions belong to the basin of attraction of a border equilibrium. However, a sustainable equilibrium can be reached when the initial conditions belong to the basin of attraction of a positive attractor. The analysis of the model shows that increasing the tourism carrying capacities can lead to different dynamical patterns. Sometimes, these patterns describe scenarios of unsustainable tourism. When this is the case, by decreasing the negative impact due to the nature and wildlife-based tourism industry, a tourism sustainability can be reached.

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Section: Introductionmentioning

confidence: 99%

Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

Villavicencio-Pulido

Vázquez–Hipólito

García‐Cruz

2022

Natural Resource Modeling

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Periodic solution of a bioeconomic fishery model by coincidence degree theory

Srivastava

Padhi²,

Domoshnitsky

2023

Electron. J. Qual. Theory Differ. Equ.

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In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics { d n d t = n ( r ( t ) ( 1 − n K ) − q ( t ) E n + D ) , d E d t = E ( A ( t ) q ( t ) α ( t ) n n + D − q 2 ( t ) α ( t ) n 2 E ( n + D ) 2 − c ( t ) ) , where the functions r , q , A , c and α are continuous positive T-periodic functions. This is the model of a coastal fishery represented as a single site with $n(t)$ is the fish stock biomass, and n(t) is the fishing effort. Examples are given to strengthen our results.

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Mathematical Model of the Dynamics of Fish, Waterbirds and Tourists in the Djoudj National Park, Senegal

Cited by 2 publications

References 10 publications

Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

Periodic solution of a bioeconomic fishery model by coincidence degree theory

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