Pattern selection in multi-layer network with adaptive coupling

Mapping Intimacies ◽

10.21203/rs.3.rs-497918/v1 ◽

2021 ◽

Author(s):

Peihua Feng ◽

Ying Wu

Keyword(s):

Adaptive Dynamics ◽

Transient State ◽

Neuron Network ◽

Neuron System ◽

Feed Forward ◽

Chimera States ◽

Chimera State ◽

Narrow Region ◽

Multiple Network ◽

Full Synchronization

Abstract Feed-forward effect modulates collective behavior of a multiple neuron network and facilitates strongly synchronization of their firing in deep layers. However, full synchronization of neuron system corresponds to functional disorder. In this work, we investigate coexistence of synchronized and incoherent neurons in deeper layer (called chimera state) in order to avoid the contradiction between facilitation of full synchronization and complete functional failure of neuron system. We focus on a multiple network containing two layers and confirm that chimera state in layer 1 could also induce that in layer 2 when the feed-forward effect is strong enough. Cluster also is discovered as a transient state which separates full synchronization and chimera state and occupy a narrow region. Both feed-forward and back-forward effect together emerge of chimera states in both layer 1 and 2 under same parameter in large range of parameters selection. Further, we introduce adaptive dynamics into inter-layer rather than intra-layer couplings. Under this circumstance chimera state still can be induced and coupling matrix will be self-organized under suitable phase parameter to guarantee chimera formation. Indeed, chimera states exist and transit to deeper layer in a regular multiple network with very strict parameter selection. The results helps understanding better the neuron firing propagating and encoding scheme in a multi-layer neuron network.

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Neuron Network Model-Based Control System Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.339.143 ◽

2013 ◽

Vol 339 ◽

pp. 143-146

Author(s):

Wei Li

Keyword(s):

Rapid Development ◽

Control Object ◽

Gain Control ◽

Neuron Network ◽

Gradual Improvement ◽

Neuron System ◽

Pid Algorithm ◽

Adaptive Neuron ◽

Single Neuron Pid ◽

Control System Model

When the control object complicate conventional PID control accuracy will be significantly reduced. In recent years, with the gradual improvement of the people of artificial intelligence theory, analog neural networks has been rapid development, the emergence of a large number of excellent algorithm and the means of achieving, from single neuron PID algorithm and with gain control neuron system PID algorithm, two aspects discusses the process of adaptive neuron PID algorithm to achieve accuracy improved adaptive neuron system controller PID algorithm based on this analysis.

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Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414400148 ◽

2014 ◽

Vol 24 (08) ◽

pp. 1440014 ◽

Cited By ~ 53

Author(s):

Yuri L. Maistrenko ◽

Anna Vasylenko ◽

Oleksandr Sudakov ◽

Roman Levchenko ◽

Volodymyr L. Maistrenko

Keyword(s):

Periodic Orbit ◽

Coupled Oscillators ◽

Phase Oscillators ◽

Invariant Circle ◽

Saddle Node Bifurcation ◽

Chimera States ◽

Chimera State ◽

Self Organized ◽

Saddle Node ◽

Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

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Chimera state in coupled map lattice of matrices

Lietuvos matematikos rinkinys ◽

10.15388/lmr.2021.25228 ◽

2021 ◽

Vol 62 ◽

pp. 57-63

Author(s):

Kotryna Mačernytė ◽

Rasa Šmidtaitė

Keyword(s):

Initial Conditions ◽

State Parameter ◽

Coupled Map Lattice ◽

Supplementary Variable ◽

Chimera States ◽

Chimera State ◽

Nilpotent Matrix ◽

Wide Range ◽

The Matrix ◽

Iterative Maps

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

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A two-layered brain network model and its chimera state

Scientific Reports ◽

10.1038/s41598-019-50969-5 ◽

2019 ◽

Vol 9 (1) ◽

Cited By ~ 4

Author(s):

Ling Kang ◽

Changhai Tian ◽

Siyu Huo ◽

Zonghua Liu

Keyword(s):

Cerebral Cortex ◽

Network Model ◽

Brain Network ◽

Clustering Coefficient ◽

Coupling Phase ◽

Chimera States ◽

Chimera State ◽

Brain Functions ◽

Coupling Strengths ◽

Left And Right

Abstract Based on the data of cerebral cortex, we present a two-layered brain network model of coupled neurons where the two layers represent the left and right hemispheres of cerebral cortex, respectively, and the links between the two layers represent the inter-couplings through the corpus callosum. By this model we show that abundant patterns of synchronization can be observed, especially the chimera state, depending on the parameters of system such as the coupling strengths and coupling phase. Further, we extend the model to a more general two-layered network to better understand the mechanism of the observed patterns, where each hemisphere of cerebral cortex is replaced by a highly clustered subnetwork. We find that the number of inter-couplings is another key parameter for the emergence of chimera states. Thus, the chimera states come from a matching between the structure parameters such as the number of inter-couplings and clustering coefficient etc and the dynamics parameters such as the intra-, inter-coupling strengths and coupling phase etc. A brief theoretical analysis is provided to explain the borderline of synchronization. These findings may provide helpful clues to understand the mechanism of brain functions.

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Minimal chimera states in phase-lag coupled mechanical oscillators

The European Physical Journal Special Topics ◽

10.1140/epjst/e2020-900270-4 ◽

2020 ◽

Vol 229 (12-13) ◽

pp. 2205-2214

Author(s):

P. Ebrahimzadeh ◽

M. Schiek ◽

P. Jaros ◽

T. Kapitaniak ◽

S. van Waasen ◽

...

Keyword(s):

Model Simulation ◽

Average Frequency ◽

Coupling Mechanism ◽

Phase Lag ◽

Time Model ◽

Chimera States ◽

Minimal Network ◽

Chimera State ◽

Saddle Type ◽

Mechanical Oscillators

Abstract We obtain experimental chimera states in the minimal network of three identical mechanical oscillators (metronomes), by introducing phase-lagged all-to-all coupling. For this, we have developed a real-time model-in-the-loop coupling mechanism that allows for flexible and online change of coupling topology, strength and phase-lag. The chimera states manifest themselves as a mismatch of average frequency between two synchronous and one desynchronized oscillator. We find this kind of striking “chimeric” behavior is robust in a wide parameter region. At other parameters, however, chimera state can lose stability and the system behavior manifests itself as a heteroclinic switching between three saddle-type chimeras. Our experimental observations are in a qualitative agreement with the model simulation.

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Symbolic Dynamics in Multidimensional Annulus and Chimera States

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414400021 ◽

2014 ◽

Vol 24 (08) ◽

pp. 1440002

Author(s):

V. S. Afraimovich ◽

L. P. Shilnikov

Keyword(s):

Symbolic Dynamics ◽

Chaotic Behavior ◽

Sufficient Conditions ◽

Invariant Set ◽

Chimera States ◽

Chimera State ◽

State Type ◽

Symbolic Sequences ◽

Angular Coordinates ◽

Low Dimensional

We derive sufficient conditions for the existence of an invariant set in an absorbing region homeomorphic to the product of a multidimensional torus and a ball. This set consists of low dimensional tori labeled by symbolic sequences. It may appear as a result of the breakdown of an attracting multidimensional torus. Trajectories on the set manifest chaotic behavior for some angular coordinates and may behave regularly for others, i.e. the dynamics on the set is of the chimera state type.

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Impact of Nonlocal Interaction on Chimera States in Nonlocally Coupled Stuart–Landau Oscillators

Complex Systems ◽

10.25088/complexsystems.30.4.513 ◽

2021 ◽

Vol 30 (4) ◽

pp. 513-524

Author(s):

K. Premalatha ◽

◽

R. Amuda ◽

V. K. Chandrasekar ◽

M. Senthilvelan ◽

...

Keyword(s):

Traveling Wave ◽

Coupled System ◽

Nonlocal Interaction ◽

Coupling Term ◽

Nonlocal Coupling ◽

Wave State ◽

Chimera States ◽

Chimera State ◽

Death State ◽

The Given

We investigate the existence of collective dynamical states in nonlocally coupled Stuart–Landau oscillators with symmetry breaking included in the coupling term. We find that the radius of nonlocal interaction and nonisochronicity parameter play important roles in identifying the swing of synchronized states through amplitude chimera states. Collective dynamical states are distinguished with the help of strength of incoherence. Different transition routes to multi-chimera death states are analyzed with respect to the nonlocal coupling radius. In addition, we investigate the existence of collective dynamical states including traveling wave state, amplitude chimera state and multi-chimera death state by introducing higher-order nonlinear terms in the system. We also verify the robustness of the given notable properties for the coupled system.

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Analyzing reactions of single mechanoenzyme molecules by light microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122538 ◽

1992 ◽

Vol 50 (1) ◽

pp. 426-427

Author(s):

Jeff Gelles

Keyword(s):

Image Processing ◽

Reaction Mechanisms ◽

Transient State ◽

Nanometer Scale ◽

Reaction Intermediates ◽

Enzyme Molecule ◽

Directed Movement ◽

Enzyme Molecules ◽

Individual Enzyme ◽

Single Reaction

Mechanoenzymes are enzymes which use a chemical reaction to power directed movement along biological polymer. Such enzymes include the cytoskeletal motors (e.g., myosins, dyneins, and kinesins) as well as nucleic acid polymerases and helicases. A single catalytic turnover of a mechanoenzyme moves the enzyme molecule along the polymer a distance on the order of 10−9 m We have developed light microscope and digital image processing methods to detect and measure nanometer-scale motions driven by single mechanoenzyme molecules. These techniques enable one to monitor the occurrence of single reaction steps and to measure the lifetimes of reaction intermediates in individual enzyme molecules. This information can be used to elucidate reaction mechanisms and determine microscopic rate constants. Such an approach circumvents difficulties encountered in the use of traditional transient-state kinetics techniques to examine mechanoenzyme reaction mechanisms.

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