Integration of mussel in fish farm: Mathematical model and analysis

The paper deals with the dynamical behavior of fish and mussel population in a fish farm where external food is supplied. The ecosystem of the fish farm is represented by a set of nonlinear differential equations involving the nutrient (food), fish and mussels. We have studied the boundedness, local stability and global stability of the model system. We have incorporated the discrete type gestational delay of fish and analyze effect of the delay on the dynamical behavior of the model system. The delay parameter complicates the dynamics depending on the external food from changing the stable state to unstable damped periodic trajectories leading to a limit cycle oscillation. We have studied the Hopf-bifurcation of the model system in the neighborhood of the coexisting equilibrium point considering delay as a variable bifurcation parameter. We have performed numerical simulation to verify the analytical results. The entire study reveals that the external food supply controls the dynamics of the system.