Bifurcation analysis on a coral-starfish model (Q2640755)

The author considers a coral-starfish model \(dN/dt=N(-2\alpha N-\delta F+\lambda),\quad dF/dt=F(2\beta N+\gamma F^ p-\epsilon),\) where N and F represent the populations of coral and starfish, respectively, and \(\lambda\),\(\epsilon\) are the intrinsic growth rates of coral and starfish, respectively. The parameters \(\alpha\),\(\delta\),\(\beta\) and \(\gamma\) are positive constants, \(0<p\leq 1\). The existence of Hopf bifurcation for this model is proved. Also, some numerical results are presented and the biological significance of the results is discussed.