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Zbl 1208.34120
Berezansky, L.; Idels, L.; Troib, L.
Global dynamics of Nicholson-type delay systems with applications. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 1, 436-445 (2011). ISSN 1468-1218

Summary: Models of marine protected areas and B-cell chronic lymphocytic leukemia dynamics that belong to the Nicholson-type delay differential systems are proposed. To study the global stability of the Nicholson-type models, we construct an exponentially stable linear system such that its solution is a solution of the nonlinear model. Explicit conditions of the existence of positive global solutions, lower and upper estimations of solutions, and the existence and uniqueness of a positive equilibrium are obtained. New results, obtained for the global stability and instability of equilibria solutions, extend known results for the scalar Nicholson models. The conditions for the stability test are quite practical, and the methods developed are applicable to the modeling of a broad spectrum of biological processes. To illustrate our finding, we study the dynamics of the fish populations in marine protected areas.

MSC 2000:: *34K60 Applications of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics

Keywords: Nicholson-type delay differential systems; global and local stability; equilibria; permanence; population dynamics; marine protected area (MPA); B-cell chronic lymphocytic leukemia (B-CLL) dynamics

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Zentralblatt MATH Berlin [Germany]