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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Desynchronization Transitions in Adaptive Networks.

Rico Berner1,2, Simon Vock1, Eckehard Schöll1,3,4

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.

Physical Review Letters
|January 29, 2021
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Summary
This summary is machine-generated.

Synchronization in adaptive networks is challenging. We developed a master stability approach to simplify this problem, revealing how network structure and adaptivity create stability islands and complex synchronization patterns.

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Area of Science:

  • Complex systems
  • Network science
  • Dynamical systems

Background:

  • Synchronization in static networks is well-understood.
  • Adaptive networks, whose connectivity changes over time, present a significant challenge for synchronization analysis.
  • Existing methods struggle to analyze synchronization in dynamic network structures.

Purpose of the Study:

  • To develop a generalizable method for analyzing synchronization in adaptive networks.
  • To decouple the effects of network topology and dynamics on synchronization.
  • To investigate the impact of network adaptivity on synchronization phenomena.

Main Methods:

  • Extension of the master stability function approach to adaptive networks.
  • Decoupling network topology from dynamical properties.
  • Analysis of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.

Main Results:

  • The master stability approach successfully reduces synchronization analysis in adaptive networks to a low-dimensional system.
  • The interplay between network adaptivity and structure leads to the formation of 'stability islands'.
  • Increasing coupling strength induces a desynchronization transition and complex partial synchronization patterns.

Conclusions:

  • The developed master stability approach provides a powerful tool for studying synchronization in a broad range of adaptive networks.
  • Network structure and adaptivity significantly influence synchronization behavior, leading to novel patterns.
  • This framework offers insights into phenomena like synaptic plasticity and their role in network dynamics.