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2009•AIP conference proceedingsRequires access

Contractivity for nonautonomous logistic equation with piecewise constant delays

Yukihiko Nakata, Masataka Kuroda, Yoshiaki Muroya, Alberto Cabada, Eduardo Liz, Juan J. Nieto

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Abstract

In this paper, we extend the result in [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] to nonautonomous logistic equations with piecewise constant arguments and establish two sufficient conditions for contractivity‐like property, from which the global asymptotic stability of the solutions of this equation is derived, even if the effect of delays dominates over the instantaneous feedback. We offer two examples to illustrate our results.

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What this paper is about

In this paper, we extend the result in [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] to nonautonomous logistic equations with piecewise constant arguments and establish two sufficient conditions for contractivity‐like property, from which the global asymptotic stability of the solutions of this equation is derived, even if the effect of delays dominates over the instantaneous feedback. We offer two examples to illustrate our results.

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Available abstract

In this paper, we extend the result in [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] to nonautonomous logistic equations with piecewise constant arguments and establish two sufficient conditions for contractivity‐like property, from which the global asymptotic stability of the solutions of this equation is derived, even if the effect of delays dominates over the instantaneous feedback. We offer two examples to illustrate our results.

Key concepts: Piecewise, Constant (computer programming), Mathematics, Exponential stability, Stability (learning theory), Logistic function, Mathematical analysis, Applied mathematics

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