Global attractivity in a “food-limited” population model with impulsive effects

Sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay-logistic equation with impulsive effect <fen><cp type="lcub" STYLE="S"><ar><r><c CSPAN="1" RSPAN="1" CA="L" RA="T">N˙(t)=r(t)N(t)<fen><cp type="lsqb" STYLE="S"><NU>K−Np(t−τ)</NU>/K+c(t)Np(t−τ)</fr><cp type="rsqb" STYLE="S"></fen>,</c></r><r><c CSPAN="1" RSPAN="1" CA="L" RA="T">N(τk+)=N(τk)<rm>exp</rm><fen><cp type="lpar" STYLE="S">Ik<fen><cp type="lpar" STYLE="S"><rm>ln</rm><fen><cp type="lpar" STYLE="S"><fr SHAPE="BUILT" ALIGN="C" STYLE="S"><NU>N(τk)</NU>/<rad><rcd>K</rcd><rdx>p</rdx></rad><cp type="rsqb" STYLE="S"></fen>,</c></r><r><c CSPAN="1" RSPAN="1" CA="L" RA="T">N(τk+)=N(τk)exp<fen><cp type="lpar" STYLE="S">Ik<fen><cp type="lpar" STYLE="S">ln<fen><cp type="lpar" STYLE="S"><NU>N(τk)</NU>/<rad><rcd>K</rcd><rdx>p</rdx></rad><cp type="rpar" STYLE="S"></fen><cp type="rpar" STYLE="S"></fen><cp type="rpar" STYLE="S"></fen>,</c></r></ar></fen> where <f>r(t)</f>, <f>c(t)</f> are continuous functions, <f>p</f>, <f>K</f>, <f>τ</f> are positive constants, and <f>{τk}k=1∞</f> denotes the sequence of impulsive time which assumed to be strictly increasing. Some special cases are also considered. [Copyright &y& Elsevier]