TY - JOUR
A2 - Simos, Theodore E.
AU - Hasanbulli, Mustafa
AU - Rogovchenko, Svitlana P.
AU - Rogovchenko, Yuriy V.
PY - 2013
DA - 2013/03/27
TI - Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting
SP - 167671
VL - 2013
AB - We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem wasstudied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter σ associated with the intensity of harvesting is explored. As σ grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.
SN - 1110-757X
UR - https://doi.org/10.1155/2013/167671
DO - 10.1155/2013/167671
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -