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Adaptive finite-time synchronization of cross-strict feedback hyperchaotic systems with parameter uncertainties

Hai-Yan Li, Yun-An Hu, Rui-Qi Wang (2013)

Kybernetika

This paper is concerned with the finite-time synchronization problem for a class of cross-strict feedback underactuated hyperchaotic systems. Using finite-time control and backstepping control approaches, a new robust adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. Appropriate adaptive laws are derived to deal with the unknown parameters of the systems. The proposed method can be applied to a variety...

Additive groups connected with asymptotic stability of some differential equations

Árpád Elbert (1998)

Archivum Mathematicum

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient λ 2 q ( s ) , s ∈ [ s 0 , ∞ ) is investigated, where λ ∈ ℝ and q ( s ) is a nondecreasing step function tending to ∞ as s → ∞ . Let S denote the set of those λ ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that S is an additive group. Four examples are given with S = { 0 } , S = ℤ , S = 𝔻 (i.e. the set of dyadic numbers), and ℚ ⊂ S ⫋ ℝ .

Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation u ( t ) = U ( t , s ) u ( s ) + ∫ s t U ( t , ξ ) f ( ξ , u ( ξ ) ) d ξ when the evolution family ( U ( t , s ) ) t ≥ s has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging...

An application of the second Lyapunov method to stability investigation of differential equations with deviations

Denis Khusainov (1998)

Archivum Mathematicum

The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand...

An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system

Makoto Hayashi (2020)

Archivum Mathematicum

In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our previous result...

Currently displaying 61 – 80 of 152