Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$ left{egin{array}{l} dfrac{partial u(t,x)}{partial t}= riangle u(t,x)-delta u(t,x)+ f(u(t- au,x)),t
eq t_k, u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),kin I_infty, end{array}ight.eqno(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of $(*)$ with Neumann boundary condition are established. These results not only are true but also improve and complement existing results for $(*)$ without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

Keywords: impulsive parabolic equation, global attractivity, oscillation