scholarly journals Chimera states for directed networks

2021 ◽  
Vol 31 (10) ◽  
pp. 103111
Author(s):  
Patrycja Jaros ◽  
Roman Levchenko ◽  
Tomasz Kapitaniak ◽  
Yuri Maistrenko
Keyword(s):  
Directed Networks ◽  
Chimera States

scholarly journals Complexity and Chimera States in a Network of Fractional-Order Laser Systems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 341
Author(s):  
Shaobo He ◽  
Hayder Natiq ◽  
Santo Banerjee ◽  
Kehui Sun
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Bifurcation Diagram ◽  
Fractional Order ◽  
Dynamical Model ◽  
Chimera States ◽  
Laser Systems ◽  
Complexity Algorithm ◽  
Derivative Order

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

scholarly journals Distributed support vector machines over dynamic balanced directed networks

2021 ◽  
pp. 1-1
Author(s):  
Mohammadreza Doostmohammadian ◽  
Alireza Aghasi ◽  
Themistoklis Charalambous ◽  
Usman A. Khan
Keyword(s):  
Support Vector Machines ◽  
Support Vector ◽  
Directed Networks ◽  
Vector Machines

scholarly journals Emergence of chimera states in a neuronal model of delayed oscillators

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Alessandra Lucchetti ◽  
Mogens H. Jensen ◽  
Mathias L. Heltberg
Keyword(s):  
Neuronal Model ◽  
Chimera States

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

Multi-headed loop chimera states in coupled oscillators

2021 ◽  
Vol 31 (1) ◽  
pp. 013135
Author(s):  
Dawid Dudkowski ◽  
Krzysztof Czołczyński ◽  
Tomasz Kapitaniak
Keyword(s):  
Coupled Oscillators ◽  
Chimera States
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