Abstract
We study the dynamics of the differential equation $$u'(t)=-\gamma u(t)+ b f(u(t-\tau))- c f(u(t-\sigma))$$ with two delayed terms, representing a positive and a negative feedback. We prove delay-dependent and absolute global stability results for the trivial and for the positive equilibrium. Our theorems provide new mathematical results as well as novel insights for several biological systems, including three-stage populations, neural models with inhibitory and excitatory loops, and the blood platelet model of Belair and Mackey. We show that, somewhat surprisingly, the introduction of a removal term with fixed delay in population models simplifies the dynamics of the equation.
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