scholarly journals Chimeras and Clusters Emerging from Robust-Chaos Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. G. Cosenza ◽  
O. Alvarez-Llamoza ◽  
A. V. Cano
Keyword(s):  
Collective Behavior ◽  
Coupled System ◽  
Coupled Systems ◽  
Response Dynamics ◽  
Local Dynamics ◽  
Chimera States ◽  
Coupled Maps

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

scholarly journals Dynamic Properties of Coupled Maps

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Chunrui Zhang ◽  
Huifeng Zheng
Keyword(s):  
Computer Simulations ◽  
Collective Behavior ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Dynamic Properties ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Theoretical Predictions ◽  
Coupling Parameters ◽  
Coupled Maps

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.

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.

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

New Pathways in Lipopolysaccharide-Induced Toll-Like Receptor 4-to-Nuclear Factor-κB Signaling Through the Coupled Uniform Sequential Reaction Systems Model

2020 ◽  
Vol 12 (10) ◽  
pp. 1246-1256
Author(s):  
Bonawentura Kochel
Keyword(s):  
Signaling Pathways ◽  
Temporal Pattern ◽  
Coupled System ◽  
Direct Consequence ◽  
Nuclear Factor Κb ◽  
Coupled Systems ◽  
Toll Like Receptor 4 ◽  
Sequential Reaction ◽  
Reaction Systems ◽  
Systems Model

The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the experimental records of activities of TLR4 downstream species IKK and NF-κB in LPS-stimulated wild-type (WT), MyD88-deficient and TRIF-deficient macrophages. New signaling pathways targeting IKK were revealed in MyD88-deficient and TRIF-deficient macrophages, and shown to be described by the coupled systems formed by 3- and 5-component or 5- and 10-component pathways, respectively. By comparing the temporal pattern of IKK in WT macrophages with those in MyD88-deficient and TRIF-deficient macrophages, two new signaling pathways, which were absent in the above defective macrophages, were found and described by a system formed by coupling 9- and 10-component pathways. As a direct consequence of the above findings, a coupled system composed of six different 3-, 5-, 5-, 9-, 10- and 10-component pathways targeting IKK and describing its temporal pattern, IKK(f), in WT macrophages was constructed. This system significantly modifies the canonical NF-κB signaling by introducing novel pathways of IKK activation. The expression of nuclear NF-κB in WT macrophages was found to depend on two different signaling pathways and to be modelled by a coupled system composed of 1- and 4-component or 2- and 8-component pathways, in dependence on sampling frequencies used in different experiments. From the three-modal NF-κB(t) temporal pattern in LPS-stimulated WT fibroblasts, three 1-, 12- and 17-component signaling pathways targeting nuclear NF-κB were determined.

Local Dynamics of Chains of Van der Pol Coupled Systems

2020 ◽  
Vol 108 (5-6) ◽  
pp. 901-905
Author(s):  
S. A. Kashchenko
Keyword(s):  
Coupled Systems ◽  
Van Der Pol ◽  
Local Dynamics

scholarly journals Chimera States in Star Networks

2016 ◽  
Vol 26 (09) ◽  
pp. 1630023 ◽  
Author(s):  
Chandrakala Meena ◽  
K. Murali ◽  
Sudeshna Sinha
Keyword(s):  
Analog Circuit ◽  
Initial Conditions ◽  
Mean Field ◽  
Coupled Systems ◽  
Dynamical Equations ◽  
Chimera States ◽  
Diffusive Coupling ◽  
Star Networks ◽  
Random Initial Conditions ◽  
Coupling Strengths

We consider star networks of chaotic oscillators, with all end-nodes connected only to the central hub node, under diffusive coupling, conjugate coupling and mean-field diffusive coupling. We observe the existence of chimeras in the end-nodes, which are identical in terms of the coupling environment and dynamical equations. Namely, the symmetry of the end-nodes is broken and coexisting groups with different synchronization features and attractor geometries emerge. Surprisingly, such chimera states are very wide-spread in this network topology, and large parameter regimes of moderate coupling strengths evolve to chimera states from generic random initial conditions. Further, we verify the robustness of these chimera states in analog circuit experiments. Thus it is evident that star networks provide a promising class of coupled systems, in natural or engineered contexts, where chimeras are prevalent.

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.

Study of Improved Multiple Discipline Feasible Strategy for Complicated System Optimization

2010 ◽  
Vol 44-47 ◽  
pp. 3264-3268 ◽  
Author(s):  
Teng Long ◽  
Li Liu ◽  
Huai Jian Li
Keyword(s):  
Computational Efficiency ◽  
Coupled System ◽  
System Optimization ◽  
Coupled Systems ◽  
Sensitivity Equation ◽  
Computation Cost ◽  
Global Sensitivity ◽  
Multiple Discipline ◽  
Complicated System ◽  
Optimization Efficiency

The advantages of global sensitivity equation (GSE) method are firstly pointed out, with which an improved multiple discipline feasible (MDF) strategy based on GSE, denoted as MDF-GSE, is developed. In MDF-GSE strategy, the sensitivity of complicated coupled system is calculated using GSE in a parallel manner, which makes MDF-GSE more efficiency when optimizing complicated coupled system compared with the original MDF strategy. Additionally, the preferable performance in convergence and robustness of MDF is also inherited in MDF-GSE. A conceptual optimization of a training airplane is executed using both MDF and MDF-GSE. The results of quantificational comparison demonstrate that computational efficiency is improved dramatically by using MDF-GSE, which makes required computation cost decreased by about 86%. The optimization time, furthermore, ulteriorly reduced due to the quasi-parallel capability of MDF-GSE. It is indicated that the MDF-GSE strategy can enhance the optimization efficiency for the complicated coupled systems.

An active vibration control model for coupled flexible systems

2008 ◽  
Vol 222 (11) ◽  
pp. 2087-2098
Author(s):  
J C Niu ◽  
A Y T Leung ◽  
C W Lim ◽  
P Q Ge
Keyword(s):  
Optimal Control ◽  
Vibration Control ◽  
State Space ◽  
Power Flow ◽  
Passive Control ◽  
Flexible Structures ◽  
Coupled System ◽  
The State ◽  
Coupled Systems ◽  
Control Force

This paper presents a novel general model for complex flexible coupled systems. In this model, parallel structures of force actuators and passive spring isolators are installed between the machine and the foundation, and some moment actuators such as piezoelectric patches are installed on the flexible foundation whose vibration cancellation feature is the key object of vibration control. This model combines active and passive control, force and moment control into a single unit to achieve the efficient vibration control of flexible structures by multiple approaches. The state-space governing equations of the coupled system are deduced. Based on the description of the state-space equation of the coupled system, the transmission paths for the power flow transmitted into the foundation are discussed in the frequency domain, and then combined into a single function. The function includes two parts: the passive and active terms, which can be conveniently employed in an optimal control strategy to achieve power flow control. The transmission characteristics of the power flow by optimal control are discussed in detail. Numerical simulations are presented to show that both force and moment controls in the analytical model can achieve substantial vibration cancellation.

Driven maps and the emergence of ordered collective behavior in globally coupled maps

1998 ◽  
Vol 58 (2) ◽  
pp. 1665-1671 ◽  
Author(s):  
A. Parravano ◽  
M. G. Cosenza
Keyword(s):  
Collective Behavior ◽  
Coupled Maps
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