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Exponential expansiveness and complete admissibility for evolution families

Mihail Megan, Bogdan Sasu, Adina Luminiţa Sasu (2004)

Czechoslovak Mathematical Journal

Connections between uniform exponential expansiveness and complete admissibility of the pair ( c 0 ( , X ) , c 0 ( , X ) ) are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.

Exponential stability and exponential instability for linear skew-product flows

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2004)

Mathematica Bohemica

We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.

Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems

Song Zheng (2020)

Kybernetika

This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems,...

Extinction in nonautonomous Kolmogorov systems

Joanna Pętela (2010)

Applicationes Mathematicae

We consider nonautonomous competitive Kolmogorov systems, which are generalizations of the classical Lotka-Volterra competition model. Applying Ahmad and Lazer's definitions of lower and upper averages of a function, we give an average condition which guarantees that all but one of the species are driven to extinction.

Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

Fengde Chen, Xiaoxing Chen, Shouying Huang (2016)

Open Mathematics

A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]....

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