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VOL. 53 | 2009 Periodicity in the May's host parasitoid equation
Walter Sizer

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

## Abstract

In this paper we consider the May's host parasitoid equation, $$\tag{1} x_{n+1} = \frac{ax_n^2}{(1 + x_n) x_{n-1}}, \alpha \gt 1.$$ We show that with initial conditions $x_{-1} = x_0 = 1$ there are values of $\alpha$ giving periodic solutions of prime period $n$ for all integers $n \geq 7$. There are no non-equilibrium periodic solutions of periods 2, 3, 4, 5 or 6.

## Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1179.39017
MathSciNet: MR2582430

Digital Object Identifier: 10.2969/aspm/05310333

Subjects:
Primary: 39A11