On the Stability of a Mathematical Model for Coral growth in a Tank

A mathematical model for coral growth in a well stirred tank is proposed based on nutrient availability. The proposed model is a system of ODEs. Stability analysis of the solutions of the system of ODEs is done for various acceptable parameter regions. Growth forms of corals in different parameter regions are observed based on the solution of the model equations. Numerical calculations and qualitative analysis reveal some interesting global behaviors such as limit cycles, homoclinic connections and heterioclinic connections of the solution trajectories. Unstable growing limit cycles are observed for some parameter values where the corresponding largest limit cycle approaches a homoclinic connection. These behaviors of the solutions of the system closely have biological consequences on coral growth.