## Differential and Integral Equations

### Attractivity properties of infinite delay Mackey-Glass type equations

#### Abstract

In this paper, several sufficient conditions are established for the global stability of the positive steady state of a scalar functional differential equation $x'=-Lx_t+f(x_t), \ x\geq 0 \; (1)$. The basic idea of the paper is to reduce an infinite dimensional system generated by $(1)$ in some "friendly" spaces to the study of associated one-dimensional maps. In this way, we improve earlier results concerning not only the scalar Lasota-Wazewska and Mackey-Glass equations with infinite distributed delay but also the multidimensional Goodwin oscillator with infinite delay.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 7 (2002), 875-896.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060803

Mathematical Reviews number (MathSciNet)
MR1895571

Zentralblatt MATH identifier
1032.34073

Subjects
Primary: 34K20: Stability theory
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]

#### Citation

Liz, Eduardo; Martínez, Clotilde; Trofimchuk, Sergei. Attractivity properties of infinite delay Mackey-Glass type equations. Differential Integral Equations 15 (2002), no. 7, 875--896. https://projecteuclid.org/euclid.die/1356060803