کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
766600 1462614 2016 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability analysis of the family of tumour angiogenesis models with distributed time delays
ترجمه فارسی عنوان
تجزیه و تحلیل ثبات خانواده مدل های آنژیوژنز تومور با تاخیر زمانی توزیع شده
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی


• A family of angiogenesis models with distributed delays is considered.
• Erlang and piecewise linear (shifted or not) delay distributions are considered.
• Stability regions of the positive steady state are investigated.
• Existences of the Hopf bifurcation phenomena are studied.
• For the limit cases stability results for models with discrete delays are recovered.

In the present paper a family of angiogenesis models that is a generalisation of the Hahnfeldt et al. model is proposed. Considered family of models consists of two differential equations with distributed time delays. The global existence and the uniqueness of the solutions are proved. Moreover, the stability of the unique positive steady state is examined in the case of Erlang and piecewise linear delay distributions. Theorems guaranteeing the existence of stability switches and occurrence of Hopf bifurcations are proved. Theoretical results are illustrated by numerical analysis performed for parameters estimated by Hahnfeldt et al. (1999) [47].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 31, Issues 1–3, February 2016, Pages 124–142
نویسندگان
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