TY - JOUR
T1 - A global attractor in some discrete contest competition models with delay under the effect of periodic stocking
AU - Alsharawi, Ziyad
PY - 2013
Y1 - 2013
N2 - We consider discrete models of the form xn+1=xnf(xn-1)+hn, where hn is a nonnegative p-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the recruitment function f(x), we give a compact invariant region and use Brouwer fixed point theorem to prove the existence of a p-periodic solution. Also, we prove the global attractivity of the p-periodic solution when p=2. In particular, this study gives theoretical results attesting to the belief that stocking (whether it is constant or periodic) preserves the global attractivity of the periodic solution in contest competition models with short delay. Finally, as an illustrative example, we discuss Pielou's model with periodic stocking.
AB - We consider discrete models of the form xn+1=xnf(xn-1)+hn, where hn is a nonnegative p-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the recruitment function f(x), we give a compact invariant region and use Brouwer fixed point theorem to prove the existence of a p-periodic solution. Also, we prove the global attractivity of the p-periodic solution when p=2. In particular, this study gives theoretical results attesting to the belief that stocking (whether it is constant or periodic) preserves the global attractivity of the periodic solution in contest competition models with short delay. Finally, as an illustrative example, we discuss Pielou's model with periodic stocking.
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U2 - 10.1155/2013/101649
DO - 10.1155/2013/101649
M3 - Article
AN - SCOPUS:84888857525
SN - 1085-3375
VL - 2013
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
M1 - 101649
ER -