Nonoccurrence of stability switching in systems of differential equations with distributed delays
Author:
Yang Kuang
Journal:
Quart. Appl. Math. 52 (1994), 569-578
MSC:
Primary 34K20; Secondary 92D25
DOI:
https://doi.org/10.1090/qam/1292206
MathSciNet review:
MR1292206
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This paper deals with stability aspects of delay differential equations with general distributed delays. The objective is to show that, frequently, general distributed delays are not harder to handle than discrete delays. This is accomplished by treating two-dimensional systems of differential delay equations with distributed delays via several different approaches. All of these approaches are general, effective, and easy to apply.
K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86, 592–627 (1982)
K. L. Cooke and P. van den Driessche, On zeros of some transcendental equations, Funkcial. Ekvac. 29, 77–90 (1986)
H. I. Freedman and K. Gopalsamy, Nonoccurrence of stability switching in systems with discrete delays, Canad. Math. Bull. 31, 52–58 (1988)
H. I. Freedman and Y. Kuang, Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac. 34, 187–209 (1991)
J. K. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977
H. W. Stech, The effect of time lags on the stability of the equilibrium state of a population growth equation, J. Math. Biol. 5, 115–120 (1978)
G. Stépán, Retarded dynamical systems: Stability and characteristic functions, Longman Scientific and Technical, Essex, 1989
K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86, 592–627 (1982)
K. L. Cooke and P. van den Driessche, On zeros of some transcendental equations, Funkcial. Ekvac. 29, 77–90 (1986)
H. I. Freedman and K. Gopalsamy, Nonoccurrence of stability switching in systems with discrete delays, Canad. Math. Bull. 31, 52–58 (1988)
H. I. Freedman and Y. Kuang, Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac. 34, 187–209 (1991)
J. K. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977
H. W. Stech, The effect of time lags on the stability of the equilibrium state of a population growth equation, J. Math. Biol. 5, 115–120 (1978)
G. Stépán, Retarded dynamical systems: Stability and characteristic functions, Longman Scientific and Technical, Essex, 1989
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
34K20,
92D25
Retrieve articles in all journals
with MSC:
34K20,
92D25
Additional Information
Article copyright:
© Copyright 1994
American Mathematical Society