Delay differential equations with Hill's type growth rate and linear harvesting

AbstractFor the equation, N˙(t)=r(t)N(t)1+[N(t)]γ−b(t)N(t)−a(t)N(g(t)),we obtain the following results: boundedness of all positive solutions, extinction, and persistence conditions. The proofs employ recent results in the theory of linear delay equations with positive and negative coefficients

Stability of Hahnfeldt Angiogenesis Models with Time Lags

Mathematical models of angiogenesis, pioneered by P. Hahnfeldt, are under study. To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies

Stability of a Time-varying Fishing Model with Delay

Abstract We introduce a delay differential equation model which describes how fish are harvested ˙N(t) = ⎣ a(t)) γ − b(t) ⎦ N(t

Periodic Solutions of Angiogenesis Models with Time Lags

To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Some open problems are presented for further studies.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Berezansky, L.. Ben Gurion University Of The Negev; IsraelFil: Idels, L.. Vancouver Island University; Canad