Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Multimachine Stability01:25

Multimachine Stability

589
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.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
589
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

7.1K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
7.1K
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

963
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.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
963
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

3.2K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
3.2K
Pole and System Stability01:24

Pole and System Stability

1.1K
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
1.1K
Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

3.5K
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
3.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Sustainability as a challenge in complex systems dynamics.

Nature computational science·2026
Same author

Extreme synchronization transitions.

Nature communications·2025
Same author

Perturbation-response dynamics of coupled nonlinear systems.

Chaos (Woodbury, N.Y.)·2024
Same author

Efficient self-organization of informal public transport networks.

Nature communications·2024
Same author

Complexified synchrony.

Chaos (Woodbury, N.Y.)·2024
Same author

Demand-driven design of bicycle infrastructure networks for improved urban bikeability.

Nature computational science·2024
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

Chaos (Woodbury, N.Y.)·2026
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Feb 23, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

12.3K

Cycle flows and multistability in oscillatory networks.

Debsankha Manik1, Marc Timme1, Dirk Witthaut2

  • 1Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.

Chaos (Woodbury, N.Y.)
|September 3, 2017
PubMed
Summary
This summary is machine-generated.

This study explores multistability in phase locked states for electrical power grids. We introduce cycle flows to analyze fixed points, finding that network structure and parameters influence the number of stable states.

More Related Videos

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
08:06

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis

Published on: March 19, 2021

3.3K
Sealable Femtoliter Chamber Arrays for Cell-free Biology
13:44

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

9.9K

Related Experiment Videos

Last Updated: Feb 23, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

12.3K
A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
08:06

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis

Published on: March 19, 2021

3.3K
Sealable Femtoliter Chamber Arrays for Cell-free Biology
13:44

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

9.9K

Area of Science:

  • Complex Systems
  • Network Science
  • Power Systems Engineering

Background:

  • Phase locked states are crucial for understanding synchronized behavior in coupled oscillator networks.
  • The Kuramoto and swing equation models are widely used to study these dynamics, particularly in electrical power grids.
  • Geometrical frustration can arise in these systems, complicating the analysis of steady states.

Purpose of the Study:

  • To investigate multistability in phase locked states within networks of phase oscillators.
  • To establish the existence of geometrically frustrated states and analyze stable fixed points.
  • To develop a formalism for bounding and computing these states in various network topologies.

Main Methods:

  • Analysis of Kuramoto and swing equation dynamics for phase oscillator networks.
  • Introduction of the cycle flow formalism to describe stable fixed points.
  • Derivation of bounds and scaling relations for fixed point counts in ring and planar networks.
  • Development of an algorithm for computing all phase locked states.

Main Results:

  • Demonstrated the existence of geometrically frustrated states where steady flow patterns lack dynamical fixed points.
  • Characterized stable fixed points using cycle flows, with phase differences limited to π/2.
  • Established that network topology (long cycles), edge weights, and parameter distribution (frequencies/injections) increase the number of fixed points.
  • Derived accurate bounds and scaling relations for fixed point counts in planar networks.

Conclusions:

  • The cycle flow formalism provides a robust method for analyzing multistability in phase locked systems.
  • Network properties significantly influence the number and stability of phase locked states in power grid models.
  • An efficient algorithm is presented for identifying all phase locked states in planar networks, aiding in grid stability assessment.