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Partial generalized synchronization theorems of differential and discrete systems

Jianyi Jing, Lequan Min, Geng Zhao (2008)

Kybernetika

This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.

Polynomial expansiveness and admissibility of weighted Lebesgue spaces

Pham Viet Hai (2021)

Czechoslovak Mathematical Journal

The paper investigates the interaction between the notions of expansiveness and admissibility. We consider a polynomially bounded discrete evolution family and define an admissibility notion via the solvability of an associated difference equation. Using the admissibility of weighted Lebesgue spaces of sequences, we give a characterization of discrete evolution families which are polynomially expansive and also those which are expansive in the ordinary sense. Thereafter, we apply the main results...

Positive solutions of third order damped nonlinear differential equations

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini (2011)

Mathematica Bohemica

We study solutions tending to nonzero constants for the third order differential equation with the damping term ( a 1 ( t ) ( a 2 ( t ) x ' ( t ) ) ' ) ' + q ( t ) x ' ( t ) + r ( t ) f ( x ( ϕ ( t ) ) ) = 0 in the case when the corresponding second order differential equation is oscillatory.

Positively homogeneous functions and the Łojasiewicz gradient inequality

Alain Haraux (2005)

Annales Polonici Mathematici

It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on ℝ N satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.

Power bounded and exponentially bounded matrices

Jaromír J. Koliha, Ivan Straškraba (1999)

Applications of Mathematics

The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.

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