Stability of Hahnfeldt Angiogenesis Models with Time Lags

Details Stability of Hahnfeldt Angiogenesis Models with Time Lags Stability of Hahnfeldt Angiogenesis Models with Time Lags

2011-05-17

arxiv.org/abs/1105.3260v1

Mathematics

Dynamical Systems

Scientific paper

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.

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