Periodic solutions of angiogenesis models with time lags

P. Amster; L. Berezansky; L. Idels

doi:10.1016/j.nonrwa.2011.07.035

Periodic solutions of angiogenesis models with time lags

P. Amster, L. Berezansky, L. Idels

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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. Numerical examples illustrate our findings. Some open problems are presented for further studies.

Original language	English
Pages (from-to)	299-311
Number of pages	13
Journal	Nonlinear Analysis: Real World Applications
Volume	13
Issue number	1
DOIs	https://doi.org/10.1016/j.nonrwa.2011.07.035
State	Published - 1 Feb 2012

Keywords

A priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonlinear nonautonomous delay differential equations
Second order Liénard type equation

ASJC Scopus subject areas

Analysis
General Engineering
General Economics, Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2011.07.035

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abstract = "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. Numerical examples illustrate our findings. Some open problems are presented for further studies.",

keywords = "A priori estimates, Angiogenesis, Existence of positive periodic solutions, LeraySchauder degree methods, Nonlinear nonautonomous delay differential equations, Second order Li{\'e}nard type equation",

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AU - Idels, L.

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N2 - 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. Numerical examples illustrate our findings. Some open problems are presented for further studies.

AB - 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. Numerical examples illustrate our findings. Some open problems are presented for further studies.

KW - A priori estimates

KW - Angiogenesis

KW - Existence of positive periodic solutions

KW - LeraySchauder degree methods

KW - Nonlinear nonautonomous delay differential equations

KW - Second order Liénard type equation

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JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

Periodic solutions of angiogenesis models with time lags

Abstract

Keywords

ASJC Scopus subject areas

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