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Global stability and the Hopf bifurcation for some class of delay differential equation
Author(s) -
Bodnar Marek,
Foryś Urszula
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.965
Subject(s) - hopf bifurcation , mathematics , delay differential equation , stability (learning theory) , class (philosophy) , differential equation , bifurcation , steady state (chemistry) , mathematical analysis , population , state (computer science) , nonlinear system , physics , chemistry , demography , algorithm , quantum mechanics , machine learning , artificial intelligence , sociology , computer science
In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Foryś ( Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd.