Abstract
We consider scalar delay differential equations $x'(t) = -\delta x(t) + f(t,x_t) \ (*)$ with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well-known Mackey--Glass-type equations, equations satisfying the Yorke condition, and equations with maxima all fall within our considerations. Here, we establish a criterion for the global asymptotical stability of a unique steady state to (*). As an example, we study Nicholson's blowflies equation, where our computations support the Smith conjecture about the equivalence between global and local asymptotical stabilities in this population model.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.