Canard limit cycles and global dynamics in a singularly perturbed predator-prey system with non-monotonic functional response (Q282010)

The author studies the predator-prey system NEWLINE\[NEWLINE\begin{aligned} {dx\over dt} &= rx\Biggl(1-{x\over k}\Biggr)- y p(x),\\ {dy\over dt} &= y(-d+ cp(x))\end{aligned}\tag{\(*\)}NEWLINE\]NEWLINE in case of the generalized Holling IV functional response NEWLINE\[NEWLINEp(x)= {mx\over ax^2+ bx+ 1}NEWLINE\]NEWLINE and for large \(r\), that means, \((*)\) is a singularly perturbed system. He determines the global dynamics of \((*)\) in dependence on the parameters. Especially, the author proves the possibility of canards generated by homoclinic bifurcation. Numerical simulations illustrate the theoretical results.