ASYMPTOTIC SYNCHRONIZATION IN LATTICES OF COUPLED NONIDENTICAL LORENZ EQUATIONS

2000 ◽  
Vol 10 (12) ◽  
pp. 2717-2728 ◽  
Author(s):  
CHUANG-HSIUNG CHIU ◽  
WEN-WEI LIN ◽  
CHEN-CHANG PENG
Keyword(s):  
Boundary Conditions ◽  
Coupled System ◽  
Lyapunov Stability Theory ◽  
Dirichlet Condition ◽  
Coupled Systems ◽  
Lorenz Equations ◽  
Trivial Equilibrium ◽  
Coupling Strengths ◽  
The Difference ◽  
Asymptotic Synchronization

In this paper we study coupled nonidentical Lorenz equations with three different boundary conditions. Coupling rules and boundary conditions play essential roles in the qualitative analysis of solutions of coupled systems. By using Lyapunov stability theory, a sufficient condition is obtained for the global stability of trivial equilibrium of coupled system with Dirichlet condition. Then we restrict our attention on the dynamics of coupled nonidentical Lorenz equations with Neumann/periodic boundary condition and prove that the asymptotic synchronization occurs provided the coupling strengths are sufficiently large. That is, the difference between any two components of solution is bounded by the quantity O(ε/ max {c1, c2, c3}) as t → ∞, where ε is the maximal deviation of parameters of nonidentical Lorenz equations, and c1, c2 and c3 are the specified coupling strengths.

A Study of Coupled Systems of ψ-Hilfer Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Ayub Samadi ◽  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated. The presented results are obtained via the classical Banach and Krasnosel’skiĭ’s fixed point theorems and the Leray–Schauder alternative. Examples are included to illustrate the effectiveness of the obtained results.

scholarly journals On Coupled Systems for Hilfer Fractional Differential Equations with Nonlocal Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Coupled Systems ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study a coupled system involving Hilfer fractional derivatives with nonlocal integral boundary conditions. Existence and uniqueness results are obtained by applying Leray-Schauder alternative, Krasnoselskii’s fixed point theorem, and Banach’s contraction mapping principle. Examples illustrating our results are also presented.

Dynamic Response of Coupled Tanks and Piping Systems Under Seismic Loading

2015 ◽  
Author(s):  
Oreste S. Bursi ◽  
Giuseppe Abbiati ◽  
Luca Caracoglia ◽  
Vincenzo La Salandra ◽  
Rocco Di Filippo ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Seismic Loading ◽  
Coupled System ◽  
Coupled Systems ◽  
Piping System ◽  
Axial Loads ◽  
Industrial Plants ◽  
Piping Systems ◽  
Uncertain Boundary

Dynamic analysis is an integral part of seismic risk assessment of industrial plants. Such analysis often neglects actual boundary conditions or proper coupling between structures of coupled systems, which introduces uncertainty into the system and may lead to erroneous results, e.g., an incorrect fragility curve, in comparison with the actual behaviour of the analyzed structure. Hence, it is important to study the effect of uncertainties on the dynamic characteristics of a system, when coupling effects are neglected. Along this line, this paper investigates the effects of uncertain boundary conditions on the dynamic response of coupled tank-piping systems subjected to seismic loading. In particular, to take into account the presence of the tank as boundary condition for the piping system, two sources of uncertainty were considered: the tank aspect ratio and the piping-to-tank attachment height ratio. Moreover, to model the seismic input, a Filtered White Noise (FWN) characterized by a Kanai-Tajimi spectrum was used. Finally, to study the dynamic interaction of a set of coupled tank-piping systems, the non-intrusive stochastic collocation (SC) technique was applied. It allowed for calculating surface responses of stresses and axial loads of a pair of components of the coupled system with a reduced number of deterministic numerical simulations.

scholarly journals First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 23
Author(s):  
João Fialho ◽  
Feliz Minhós
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Existence Results ◽  
Coupled Systems ◽  
First Order ◽  
Sirs Model ◽  
Functional Boundary ◽  
Functional Boundary Conditions

The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundary conditions. Functional boundary conditions, which are becoming increasingly popular in the literature, as they generalize most of the classical cases and in addition can be used to tackle global conditions, such as maximum or minimum conditions. The arguments used are based on the Arzèla Ascoli theorem and Schauder’s fixed point theorem. The existence results are directly applied to an epidemic SIRS (Susceptible-Infectious-Recovered-Susceptible) model, with global boundary conditions.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation

2021 ◽  
Vol 11 (10) ◽  
pp. 4589
Author(s):  
Ivan Duvnjak ◽  
Domagoj Damjanović ◽  
Marko Bartolac ◽  
Ana Skender
Keyword(s):  
Boundary Conditions ◽  
Damage Detection ◽  
Mode Shape ◽  
Experimental Validation ◽  
Detection Method ◽  
Dynamic Properties ◽  
Damage Index ◽  
Main Principle ◽  
The Difference ◽  
Different Levels

The main principle of vibration-based damage detection in structures is to interpret the changes in dynamic properties of the structure as indicators of damage. In this study, the mode shape damage index (MSDI) method was used to identify discrete damages in plate-like structures. This damage index is based on the difference between modified modal displacements in the undamaged and damaged state of the structure. In order to assess the advantages and limitations of the proposed algorithm, we performed experimental modal analysis on a reinforced concrete (RC) plate under 10 different damage cases. The MSDI values were calculated through considering single and/or multiple damage locations, different levels of damage, and boundary conditions. The experimental results confirmed that the MSDI method can be used to detect the existence of damage, identify single and/or multiple damage locations, and estimate damage severity in the case of single discrete damage.

On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems

2003 ◽  
Vol 10 (3) ◽  
pp. 401-410
Author(s):  
M. S. Agranovich ◽  
B. A. Amosov
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Fourier Coefficients ◽  
Elliptic Boundary ◽  
A Priori ◽  
Adjoint Problem ◽  
Elliptic Boundary Value ◽  
Right Hand ◽  
The Difference ◽  
The Right

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

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