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Dynamical study of effects of herbivores on corals and algae in a coral reef ecosystem

Banamali Maji, Samares Pal

Abstract



It is well known that coral reefs are at a high risk of destruction fromterrestrial runoff, various anthropogenic activities and pollution in marine ecosystem. The growth of coral reef and macro algae depend on the activities of herbivores on it. Here, we introduce a mathematical model to explain the effect of activities of herbivores on growth of coral reef and macro algae in a coral reef ecosystem and investigate the time dependent sensitivity index of
parameters on different species.A detailed analysis of the model reveals that the system undergoes a Hopf-bifurcation when the rate of decline of herbivorous fishes pass through its critical value. Competition for space and light between coral and algae in herbivore free
system is derived conducting analytical study of the model and coexistence between corals and algae is also illustrated using numerical simulations.

Keywords


Hopf-bifurcation, Competitiveness, Sensitivity analysis, Sensitivity index, Coexistence.

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