scholarly journals Synchronization in Networks With Heterogeneous Adaptation Rules and Applications to Distance-Dependent Synaptic Plasticity

2021 ◽  
Vol 7 ◽  
Author(s):  
Rico Berner ◽  
Serhiy Yanchuk
Keyword(s):  
Synaptic Plasticity ◽  
Long Range ◽  
Network Structure ◽  
Function Approach ◽  
Adaptive Networks ◽  
Ring Networks ◽  
Phase Oscillators ◽  
Stability Function ◽  
Master Stability Function ◽  
Adaptation Rules

This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with distance-dependent adaptations. For this system, we extend the master stability function approach to adaptive networks with heterogeneous adaptation. Our method allows for separating the contributions of network structure, local node dynamics, and heterogeneous adaptation in determining synchronization. Utilizing our proposed methodology, we explain mechanisms leading to synchronization or desynchronization by enhanced long-range connections in nonlocally coupled ring networks and networks with Gaussian distance-dependent coupling weights equipped with a biologically motivated plasticity rule.

scholarly journals Synchronizability of Multi-Layer Dual-Center Coupled Star Networks

2021 ◽  
Vol 9 ◽  
Author(s):  
Jian Zhu ◽  
Da Huang ◽  
Zhiyong Yu ◽  
Ping Pei
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Network Structure ◽  
Single Layer ◽  
Ring Networks ◽  
Laplacian Spectrum ◽  
Single Center ◽  
Stability Function ◽  
Star Networks ◽  
Theoretical Results

In the research on complex networks, synchronizability is a significant measurement of network nature. Several research studies center around the synchronizability of single-layer complex networks and few studies on the synchronizability of multi-layer networks. Firstly, this paper calculates the Laplacian spectrum of multi-layer dual-center coupled star networks and multi-layer dual-center coupled star–ring networks according to the master stability function (MSF) and obtains important indicators reflecting the synchronizability of the above two network structures. Secondly, it discusses the relationships among synchronizability and various parameters, and numerical simulations are given to illustrate the effectiveness of the theoretical results. Finally, it is found that the two sorts of networks studied in this paper are of the same synchronizability, and compared with that of a single-center network structure, the synchronizability of two dual-center structures is relatively weaker.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

scholarly journals A master stability function approach to cardiac alternans

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Yi Ming Lai ◽  
Joshua Veasy ◽  
Stephen Coombes ◽  
Rüdiger Thul
Keyword(s):  
Activity Patterns ◽  
Muscle Cells ◽  
Stability Function ◽  
Cardiac Muscle Cells ◽  
Network Nodes ◽  
Master Stability Function ◽  
Synchronous Network ◽  
Cardiac Alternans ◽  
Regular Rhythm ◽  
Network Of Networks

Abstract During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a variety of cardiac arrhythmias including cardiac alternans. Here, we focus on so-called microscopic calcium alternans and show how their complex spatial patterns can be understood with the help of the master stability function. Our work makes use of the fact that cardiac muscle cells can be conceptualised as a network of networks, and that calcium alternans correspond to an instability of the synchronous network state. In particular, we demonstrate how small changes in the coupling strength between network nodes can give rise to drastically different activity patterns in the network.

scholarly journals Synchrony in networks of coupled non-smooth dynamical systems: Extending the master stability function

2016 ◽  
Vol 27 (6) ◽  
pp. 904-922 ◽  
Author(s):  
STEPHEN COOMBES ◽  
RÜDIGER THUL
Keyword(s):  
Dynamical Systems ◽  
Variational Equation ◽  
Period Doubling ◽  
Star Graph ◽  
Stability Function ◽  
Bifurcation Of Limit Cycles ◽  
Master Stability Function ◽  
Coupled Networks ◽  
Low Dimensional ◽  
Insight Into

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbit. For smooth dynamical systems, this orbit is not generically available in closed form. However, many models in physics, engineering and biology admit to non-smooth piece-wise linear caricatures, for which it is possible to construct periodic orbits without recourse to numerical evolution of trajectories. A classic example is the McKean model of an excitable system that has been extensively studied in the mathematical neuroscience community. Understandably, the master stability function cannot be immediately applied to networks of such non-smooth elements. Here, we show how to extend the master stability function to non-smooth planar piece-wise linear systems, and in the process demonstrate that considerable insight into network dynamics can be obtained. In illustration, we highlight an inverse period-doubling route to synchrony, under variation in coupling strength, in globally linearly coupled networks for which the node dynamics is poised near a homoclinic bifurcation. Moreover, for a star graph, we establish a mechanism for achieving so-called remote synchronisation (where the hub oscillator does not synchronise with the rest of the network), even when all the oscillators are identical. We contrast this with node dynamics close to a non-smooth Andronov–Hopf bifurcation and also a saddle node bifurcation of limit cycles, for which no such bifurcation of synchrony occurs.

scholarly journals Relay Synchronization in a Weighted Triplex Network

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2135
Author(s):  
Md Sayeed Anwar ◽  
Dibakar Ghosh ◽  
Nikita Frolov
Keyword(s):  
Topological Property ◽  
Strong Influence ◽  
Clustering Coefficient ◽  
The Other ◽  
Function Approach ◽  
Stability Conditions ◽  
Stability Function ◽  
Multiplex Network ◽  
Low Degree ◽  
High Degree

Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting.

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