Absence of limit cycles of a predator-prey system with a sigmoid functional response Original Research Article

A large number of studies have been made on the predator-prey system with Hollingʹs functional response, namely, View the MathML source. This paper presents a sufficient condition under which the predator-prey system has no limit cycles for n = 3. The argument used here is based on a result of Liénard dynamics. The relation between previous results (n = 1,2) and our result (n = 3) is cleared. Some phase portraits of trajectories of the predator-prey system are also given as an example of our result.