Abstract:
The logistic equation with delay and diffusion, which is important in mathematical ecology, is considered. It is assumed that the boundary conditions at one end of the interval $[0,1]$ contain a parameter. The question of local — in the neighborhood of the equilibrium state — dynamics of the corresponding boundary value problem for all values of the boundary condition parameters is investigated. Critical cases in the problem of stability of the equilibrium state are identified and normal forms — scalar complex ordinary differential equations of the first order — are constructed. Their nonlocal dynamics determine the behavior of solutions of the original problem in a small neighborhood of the equilibrium state.
Keywords:logistic equation, normal form, lag, dynamics, algorithm.
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