SciELO - Scientific Electronic Library Online

 
vol.15 número3Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

Compartir


Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.15 no.3 Temuco  2013

http://dx.doi.org/10.4067/S0719-06462013000300001 

 

An Elementary Study of a Class of Dynamic Systems with Single Time Delay


Akio Matsumoto1 and Ferenc Szidarovszky2

1Chuo University, Department of Economics, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan. akiom@tamacc.chuo-u.ac.jp

2University of Pecs, Department of Applied Mathematics, Pecs, Ifjusag u. 6, H-7624, Pecs,Hungary szidarka@gmail.com


ABSTRACT

A complete eigenvalue analysis is given for a certain class of dynamic systems with a single delay. The stability region is determined and it is demonstrated that there is only one stability switch. Special cases from economics, biology and engineering illustrate the importance of such models.

Keywords and Phrases: dynamic systems, time delay, stability.


RESUMEN

Un análisis completo de los autovalores se entrega para una clase de sistemas dinámicos con retardo simple. La región de estabilidad se determina y se demuestra que existe solamente un switch de estabilidad. Casos especiales para Economía, Biología e Ingeniería ilustran la importancia de los modelos mencionados.

2010 AMS Mathematics Subject Classification: 34K20, 37C75.



References

[1] Burger, E. (1956), On the Stability of Certain Economic Systems. Econometrica, 24(4), 488-493.         [ Links ]

[2] Cushing, J. M. (1977), Integro-Differential Equations and Delay Models in Population Dynamics. Springer-Verlag, Berlin/Heidelberg/New York.         [ Links ]

[3] Hale, J. (1979), Nonlinear Oscillations in Equations with Delays. In Nonlinear Oscillations in Biology (K. C. Hoppenstadt, ed.), Lectures in Applied Mathematics, 17, 157-185.         [ Links ]

[4] Hale, J. and W. Huang (1993), Global Geometry of the Stable Regions for Two Delay Differential Equations. J. of Math. Analysis and Appl., 178, 344-362.         [ Links ]

[5] Hayes, N. D. (1950), Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation. J. of the London Math. Society, 25, 226-232.         [ Links ]

[6] Invernizzi, S. and A. Medio (1991), On Lags and Chaos in Economic Dynamic Models. Journal of Math. Econ., 20, 521-550.         [ Links ]

[7] Piotrowska. M. (2007), A Remark on the ODE with Two Discrete Delays. Journal of Math. Analysis and Appl., 329, 664-676.         [ Links ]


Received: July 2011 / Accepted: October 2012.

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons