Аннотация:We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear problem, and in this case the positive equilibrium is always unstable. We obtain a necessary and sufficient condition for the existence of blow-up solutions, and characterize a wide class of such solutions. There is a parameter set such that the non-trivial equilibrium is locally stable but not globally stable due to the co-existence with blow-up solutions.
Издательство:American Institute of Mathematical Sciences
Источник:Communications on Pure & Applied Analysis
Ключевые слова:Mathematical and Theoretical Epidemiology and Ecology Models, Stability and Controllability of Differential Equations, Nonlinear Differential Equations Analysis
