Applications of Mathematics, first online, pp. 1-36

Herbivore harvesting and alternative steady states in coral reefs

Ikbal Hossein Sarkar, Joydeb Bhattacharyya, Samares Pal

Received December 3, 2019.   Published online December 16, 2020.

Abstract:  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.
Keywords:  phase shift; coral bleaching; harvesting; Hopf bifurcation
Classification MSC:  34A34, 34D20, 92D25
DOI:  10.21136/AM.2020.0338-19

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Affiliations:   Ikbal Hossein Sarkar, Department of Mathematics, Government General Degree College at Pedong, Pedong, Kalimpong, West Bengal 734311, India, e-mail:; Joydeb Bhattacharyya, Department of Mathematics, Karimpur Pannadevi College, Nadia, Ramkrishnapally, Karimpur, West Bengal 741152, India, e-mail:; Samares Pal (corresponding author), Department of Mathematics, University of Kalyani, Kalyani 741235, India, e-mail:

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