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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

Sze-Bi Hsu 1, , Ming-Chia Li 2, , Weishi Liu 3, and  Mikhail Malkin 4,

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.
Keywords: singular perturbation., global oscillation, Nicholson-Bailey model, heteroclinic foliation, delay of stability loss.
Mathematics Subject Classification: 37E30, 39A11, 92D2.
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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