Asymptotic stability for delayed logistic type equations

Authors:
Teresa Faria
Affiliations:
Departamento de Matemática and CMAF, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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Abstract

We study the stability of scalar delayed equations of logistic type with a positive equilibrium and a linear logistic term. The global asymptotic stability of the positive equilibrium, called the carrying capacity, is proven imposing a condition on a negative feedback term without delay dominating the delayed effect. It turns out that this assumption is a necessary and sufficient condition for the linearized equation about the positive equilibrium to be asymptotically stable, globally in the delays. The global stability of more general scalar delay differential equations is also addressed.