TY - JOUR

T1 - Stability of a time-varying fishing model with delay

AU - Berezansky, L.

AU - Idels, L.

N1 - Funding Information:
The authors would like to extend their appreciation to the anonymous referee for the helpful suggestions which have greatly improved this paper. The first author’s research was supported in part by the Israeli Ministry of Absorption and the second author’s research was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - To incorporate ecosystem effects, environmental variability and other factors that affect the population growth, the periodicity of the parameters of the model is assumed. We introduce a delay differential equation model which describes how fish are harvested: (A)over(N, ̇) (t) = [frac(a (t), 1 + (frac(N (θ (t)), K (t)))γ) - b (t)] N (t) . In our previous studies the persistence of Eq. (A) and the existence of a periodic solution to this equation were investigated. In the present paper the explicit conditions of global attractivity of the positive periodic solutions to Eq. (A) are obtained. It will also be shown that if the stability conditions are violated, the model exhibits sustained oscillations.

AB - To incorporate ecosystem effects, environmental variability and other factors that affect the population growth, the periodicity of the parameters of the model is assumed. We introduce a delay differential equation model which describes how fish are harvested: (A)over(N, ̇) (t) = [frac(a (t), 1 + (frac(N (θ (t)), K (t)))γ) - b (t)] N (t) . In our previous studies the persistence of Eq. (A) and the existence of a periodic solution to this equation were investigated. In the present paper the explicit conditions of global attractivity of the positive periodic solutions to Eq. (A) are obtained. It will also be shown that if the stability conditions are violated, the model exhibits sustained oscillations.

KW - Delay differential equations

KW - Fishery

KW - Global and local stability

KW - Periodic environment

UR - http://www.scopus.com/inward/record.url?scp=41049116887&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2007.03.027

DO - 10.1016/j.aml.2007.03.027

M3 - Article

AN - SCOPUS:41049116887

VL - 21

SP - 447

EP - 452

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 5

ER -