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...
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| creator | Amster, P Berezansky, L Idels, L |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1105.3260 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.1105.3260</doi><oa>free_for_read</oa></addata></record> |
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| title | Stability of Hahnfeldt Angiogenesis Models with Time Lags |
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