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Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification

Xiaobing Zhou, Murong Jiang, Yaqun Huang (2014)

Kybernetika

This paper investigates adaptive switched modified function projective synchronization between two complex nonlinear hyperchaotic systems with unknown parameters. Based on adaptive control and parameter identification, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve switched modified function projective synchronization between two different complex nonlinear hyperchaotic systems and to estimate the unknown system parameters. A numerical simulation...

Symmetries and solvability of linear differential equations.

Luis Joaquín Boya, F. González-Gascón (1980)

Revista Matemática Hispanoamericana

The canonical form theorem, applied to a certain group of symmetry transformations of certain Fuchsian equations, leads automatically to the integration of them. The result can be extended to any n-order differential equation possesing a certain pointlike group of symmetries with a maximal abelian Lie-subgroup of order c.

Synchronization of fractional-order chaotic systems with multiple delays by a new approach

Jianbing Hu, Hua Wei, Lingdong Zhao (2015)

Kybernetika

In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.

Synchronization with error bound of non-identical forced oscillators

Jian Gen Wang, Jianping Cai, Mihua Ma, Jiuchao Feng (2008)

Kybernetika

Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.

Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDP

Denis Serre (1989)

Annales de l'institut Fourier

Lorsque tous les champs caractéristiques d’un système hyperbolique riche sont linéairement dégénérés, les opérateurs résolvants sont bien définis et opèrent sur l’ensemble des solutions de certains systèmes d’équations différentielles ordinaires. Celles-ci peuvent être implicites ou explicites. Dans le cas implicite, on montre que toutes les solutions sont presque-périodiques; de plus elles seront toutes périodiques pourvu que l’une d’entre elles le soit. Dans le cas explicite, on définit un opérateur...

Tame semiflows for piecewise linear vector fields

Daniel Panazzolo (2002)

Annales de l’institut Fourier

Let ℰ be a disjoint decomposition of ℝ n and let X be a vector field on ℝ n , defined to be linear on each cell of the decomposition ℰ . Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure ℝ an , exp . In particular, when X is a continuous vector field and Γ is an invariant subset of X , our result implies that if Γ is non-spiralling then the Poincaré first return map associated Γ is also in ℝ an , exp .

Tauberian theorems for vector-valued Fourier and Laplace transforms

Ralph Chill (1998)

Studia Mathematica

Let X be a Banach space and f ∈ L l 1 o c ( ℝ ; X ) be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.

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