Embedded invariant manifolds and ordering of chaotic synchronization of diffusively coupled systems

2002 ◽  
Author(s):  
I.V. Belykh ◽  
V.N. Belykh
Keyword(s):  
Invariant Manifolds ◽  
Chaotic Synchronization ◽  
Coupled Systems

scholarly journals Invariant manifolds and cluster synchronization in a family of locally coupled map lattices

2000 ◽  
Vol 4 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Vladimir belykh ◽  
Igor Blykh ◽  
Nikolai Komrakov ◽  
Erik Moseklide
Keyword(s):  
Invariant Manifolds ◽  
Variational Equation ◽  
Chaotic Synchronization ◽  
Discrete Dynamical Systems ◽  
Cluster Synchronization ◽  
Coupled Map Lattices ◽  
Self Similarity ◽  
Different Types ◽  
Coupled Maps ◽  
The Stability

This paper presents an analysis of the invariant manifolds for a general family of locally coupled map lattices. These manifolds define the different types of full, partial, and anti-phase chaotic synchronization that can arise in discrete dynamical systems. Existence of various invariant manifolds, self-similarity as well as orderings and embeddings of the manifolds of a coupled map array are established. A general variational equation for the stability analysis of invariant manifolds is derived, and stability conditions for full and partial chaotic synchronization of concrete coupled maps are obtained. The general results are illustrated through examples of three coupled two-dimensional standard maps with damping.

Experimental Minimization of Power Absorption in Chaotic Synchronization

2019 ◽  
Vol 22 (4) ◽  
pp. 401-406
Author(s):  
Arturo Buscarino ◽  
Carlo Famoso ◽  
Luigi Fortuna ◽  
Mattia Frasca
Keyword(s):  
Power Dissipation ◽  
Chaotic Synchronization ◽  
Coupled Systems ◽  
Power Absorption ◽  
Synchronous State ◽  
Experimental Findings ◽  
The Relationship ◽  
The Way

In this paper some recent experimental findings on chaotic synchronization are discussed showing how power absorption is minimum when the synchronous state is reached. The case of two Chua’s circuits is then theoretically dealt with confirming that synchronization minimizes power dissipation. The relationship between synchronization and power absorption, highlighted in such experiments and in the analysis presented, paves the way to new interpretations of synchronization in two or more coupled systems.

scholarly journals Метод определения характеристик перемежающейся обобщенной синхронизации, основанный на вычислении вероятности наблюдения синхронного режима

2022 ◽  
Vol 48 (2) ◽  
pp. 3
Author(s):  
О.И. Москаленко ◽  
А.А. Короновский ◽  
А.О. Сельский ◽  
Е.В. Евстифеев
Keyword(s):  
Chaotic Synchronization ◽  
Coupled Systems ◽  
The Other ◽  
Generalized Synchronization ◽  
Synchronization Regime

Method to define the characteristic phases in the behavior of unidirectionally coupled systems being near the boundary of the generalized chaotic synchronization regime onset, based on calculation of the probability of the synchronous regime observation in ensemble of coupled systems is proposed. Using the example of unidirectionally coupled Rössler systems in the band chaos regime we show its efficiency in comparison with the other known methods for detection the characteristics of intermittent generalized synchronization.

scholarly journals Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

2017 ◽  
Vol 27 (14) ◽  
pp. 1730050 ◽  
Author(s):  
J. D. Mireles James ◽  
Maxime Murray
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Invariant Manifolds ◽  
Posteriori Error ◽  
Coupled Systems ◽  
Parameterization Method ◽  
Taylor Coefficients ◽  
Unstable Manifolds ◽  
Linear Differential ◽  
Posteriori Error Analysis

This paper develops a Chebyshev–Taylor spectral method for studying stable/unstable manifolds attached to periodic solutions of differential equations. The work exploits the parameterization method — a general functional analytic framework for studying invariant manifolds. Useful features of the parameterization method include the fact that it can follow folds in the embedding, recovers the dynamics on the manifold through a simple conjugacy, and admits a natural notion of a posteriori error analysis. Our approach begins by deriving a recursive system of linear differential equations describing the Taylor coefficients of the invariant manifold. We represent periodic solutions of these equations as solutions of coupled systems of boundary value problems. We discuss the implementation and performance of the method for the Lorenz system, and for the planar circular restricted three- and four-body problems. We also illustrate the use of the method as a tool for computing cycle-to-cycle connecting orbits.

Terrorist teams as loosely coupled systems.

2018 ◽  
Vol 73 (4) ◽  
pp. 491-503 ◽  
Author(s):  
Matthias Spitzmuller ◽  
Guihyun Park
Keyword(s):  
Coupled Systems ◽  
Loosely Coupled Systems ◽  
Loosely Coupled

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 Revealing the Challenges of Smart Rainwater Harvesting for Integrated and Digital Resilience of Urban Water Infrastructure

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1902
Author(s):  
Martin Oberascher ◽  
Aun Dastgir ◽  
Jiada Li ◽  
Sina Hesarkazzazi ◽  
Mohsen Hajibabaei ◽  
...  
Keyword(s):  
Large Scale ◽  
Rainwater Harvesting ◽  
Data Communication ◽  
Integrated System ◽  
Coupled Systems ◽  
Urban Resilience ◽  
System Failures ◽  
Household Level ◽  
Performance Improvements ◽  
Smart Water

Smart rainwater harvesting (RWH) systems can automatically release stormwater prior to rainfall events to increase detention capacity on a household level. However, impacts and benefits of a widespread implementation of these systems are often unknown. This works aims to investigate the effect of a large-scale implementation of smart RWH systems on urban resilience by hypothetically retrofitting an Alpine municipality with smart rain barrels. Smart RWH systems represent dynamic systems, and therefore, the interaction between the coupled systems RWH units, an urban drainage network (UDN) and digital infrastructure is critical for evaluating resilience against system failures. In particular, digital parameters (e.g., accuracy of weather forecasts, or reliability of data communication) can differ from an ideal performance. Therefore, different digital parameters are varied to determine the range of uncertainties associated with smart RWH systems. As the results demonstrate, smart RWH systems can further increase integrated system resilience but require a coordinated integration into the overall system. Additionally, sufficient consideration of digital uncertainties is of great importance for smart water systems, as uncertainties can reduce/eliminate gained performance improvements. Moreover, a long-term simulation should be applied to investigate resilience with digital applications to reduce dependence on boundary conditions and rainfall patterns.

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