Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments
In this paper, a logistic equation with multiple piecewise constant arguments is investigated in detail. We generalize the approach in two papers, [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2) (2...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/462 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/462 |
| Access Level: | acceso abierto |
| Palabra clave: | 3/2 type stability Difference equations Global asymptotic stability Logistic equation Piecewise constant arguments Time delays |
| Sumario: | In this paper, a logistic equation with multiple piecewise constant arguments is investigated in detail. We generalize the approach in two papers, [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2) (2004) 560580] and [Y. Muroya, E. Ishiwata, N. Guglielmi, Global stability for nonlinear difference equations with variable coefficients, J. Math. Anal. Appl. 334 (1) (2007) 232247], and establish a new condition for the global stability of the equation. Their results are given as one of the special cases. Moreover, we improve the 3/2 type stability condition under several dominance assumptions on the coefficients of the equation. Some examples and numerical simulations are also presented. All of these examples show that there are several conditions for the global stability of the equation, depending on the coefficients on the delay terms of the equation, beyond the 3/2 type stability condition. |
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