# American Institute of Mathematical Sciences

November  2003, 9(6): 1465-1492. doi: 10.3934/dcds.2003.9.1465

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

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

Received  September 2002 Revised  June 2003 Published  September 2003

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.
Citation: Sze-Bi Hsu, Ming-Chia Li, Weishi Liu, Mikhail Malkin. Heteroclinic foliation, global oscillations for the Nicholson-Bailey model and delay of stability loss. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1465-1492. doi: 10.3934/dcds.2003.9.1465
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