scholarly journals Analysis of parameter mismatches in the master stability function for network synchronization

2011 ◽  
Vol 93 (5) ◽  
pp. 50002 ◽  
Author(s):  
F. Sorrentino ◽  
M. Porfiri
Keyword(s):  
Stability Function ◽  
Network Synchronization ◽  
Master Stability Function

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 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.

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