Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

An, Qi¹  Beretta, Edoardo²  Kuang, Yang³  Wang, Chuncheng¹  Wang, Hao⁴ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

[2] CIMAB Interuniv Ctr Math Appl Biol Med & Environm, Paderno Del Grappa, Italy

[3] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[4] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

关键词: Delay differential equation;    Stability switch;    Characteristic equation;    Epidemic model;   

DOI  :  10.1016/j.jde.2018.11.025

来源: Elsevier

【 摘 要 】

Most modeling efforts involve multiple physical or biological processes. All physical or biological processes take time to complete. Therefore, multiple time delays occur naturally and shall be considered in more advanced modeling efforts. Carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters. However, a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent. The main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay. In addition to simple and illustrative examples, we present a detailed application of our method to the study of a two discrete delay SIR model. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free