Heteroclinic foliation, global oscillations for the Nicholson-Bailey model and delay of stability loss

Sze-Bi Hsu; Ming-Chia Li; Weishi Liu; Mikhail Malkin

doi:10.3934/dcds.2003.9.1465

Article Contents

2003, Volume 9, Issue 6: 1465-1492. Doi: 10.3934/dcds.2003.9.1465

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Heteroclinic foliation, global oscillations for the Nicholson-Bailey model and delay of stability loss

1.
Department of Mathematics, National Tsing Hua University, Hsinchu 300
2.
Department of Mathematics, National Changhua University of Education, Changhua 500
3.
Department of Mathematics, University of Kansas, Lawrence, KS 66045
4.
Department of Mathematics, Nizhny Novgorod State University, Nizhny Novgorod

Received: August 31, 2002

Revised: May 31, 2003

Published: October 2003

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Abstract

This paper is concerned with the classical Nicholson-Bailey model [15] defined by $f_\lambda(x,y)=(y(1-e^{-x}), \lambda y e^{-x})$. We show that for $\lambda=1$ a heteroclinic foliation exists and for $\lambda>1$ global strict oscillations take place. The important phenomenon of delay of stability loss is established for a general class of discrete dynamical systems, and it is applied to the study of nonexistence of periodic orbits for the Nicholson-Bailey model.

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Mathematics Subject Classification: 37E30, 39A11, 92D25.

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