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Multimachine Stability01:25

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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Related Experiment Video

Updated: Apr 18, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Phase multistability in a dynamical small world network.

A V Shabunin1

  • 1Radiophysics and Nonlinear Dynamics Department, Saratov State University, Saratov, Russia.

Chaos (Woodbury, N.Y.)
|February 2, 2015
PubMed
Summary

Phase multistability in complex networks is investigated. Increasing non-local links in oscillatory networks leads to phase fluctuations and cluster formation, ultimately eliminating multistability for an in-phase state.

Area of Science:

  • Complex networks
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Phase multistability is a phenomenon observed in coupled oscillatory systems.
  • Small-world networks exhibit unique topological properties influencing system dynamics.
  • Diffusive couplings and network structure play critical roles in emergent behaviors.

Purpose of the Study:

  • To investigate the impact of dynamic non-local couplings on phase multistability in a small-world network.
  • To model the spontaneous emergence and vanishing of links in a network.
  • To understand the transition of network states under varying coupling conditions.

Main Methods:

  • Simulations of a small-world network composed of periodic oscillators with diffusive couplings.
  • Modeling of dynamic coupling using birth and death stochastic processes via a cellular automaton approach.

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  • Analysis of network evolution with gradually increasing non-local links.

    • Main Results:

    • The network transitions through stages of phase fluctuations and spatial cluster formation as non-local couplings increase.
    • The presence of dynamic non-local couplings leads to the suppression of phase multistability.
    • The in-phase synchronization regime ultimately dominates the network dynamics.

    Conclusions:

    • Dynamic non-local couplings disrupt phase multistability in small-world oscillatory networks.
    • The network dynamics are sensitive to the interplay between network topology and coupling mechanisms.
    • The in-phase state is a robust attractor in this system under extensive non-local coupling.