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Global stability for a class of functional differential equations (Application to Nicholson's blowflies and Mackey-Glass models)

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  • Global asymptotic and exponential stability of equilibria for the following class of functional differential equations with distributed delay is investigated

    $ x'(t)=-f(x(t))+\int_{0}^{\tau}h(a)g(x(t-a))da.$

    We make our analysis by introducing a new approach, combining a Lyapunov functional and monotone semiflow theory. The relevance of our results is illustrated by studying the well-known integro-differential Nicholson's blowflies and Mackey-Glass equations, where some delay independent stability conditions are provided. Furthermore, new results related to exponential stability region of the positive equilibrium for these both models are established.

    Mathematics Subject Classification: Primary: 34K20, 37L15; Secondary: 92B05.


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