Geodesic
Herbivore harvesting and alternative steady states in coral reefs
Applications of Mathematics, Tome 66 (2021) no. 2, pp. 233-268 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.
Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.
DOI : 10.21136/AM.2020.0338-19
Classification : 34A34, 34D20, 92D25
Keywords: phase shift; coral bleaching; harvesting; Hopf bifurcation 
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     title = {Herbivore harvesting and alternative steady states in coral reefs},
     journal = {Applications of Mathematics},
     pages = {233--268},
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Sarkar, Ikbal Hossein; Bhattacharyya, Joydeb; Pal, Samares. Herbivore harvesting and alternative steady states in coral reefs. Applications of Mathematics, Tome 66 (2021) no. 2, pp. 233-268. doi: 10.21136/AM.2020.0338-19

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