Related Experiment Video
Updated: Jun 5, 2026
05:59
New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies
Published on: October 6, 2023
From incoherence to synchronicity in the network Kuramoto model
1Defence Science and Technology Organisation, Canberra, Australian Capital Territory, Australia. alexander.kalloniatis@dsto.defence.gov.au
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We analyzed the Kuramoto model
Area of Science:
- Complex systems
- Dynamical systems theory
- Network science
Background:
- The Kuramoto model describes synchronization in coupled oscillators.
- Distinguishing self-synchronization from its stability is crucial.
- Stability analysis typically involves fluctuations around fixed points.
Purpose of the Study:
- To differentiate self-synchronization from stability in the Kuramoto model.
- To analyze stability using graph Laplacian modes.
- To identify critical couplings for deviations from classical stability.
Main Methods:
- Analysis of graph Laplacian modes for Lyapunov stability.
- Reduction of dynamical equations to population models (logistic, Lotka-Volterra).
- Analytical derivation of critical couplings.
Main Results:
- Lyapunov stability of the phase-synchronized fixed point demonstrated.
- Identification of an intermediate regime between incoherence and synchronization.
- Existence of stable, unstable, and hyperbolic fixed points in this regime.
Conclusions:
- The study analytically explains the intermediate regime in oscillator synchronization.
- New critical couplings are derived, signaling stability deviations.
- Results are discussed in the context of various network structures.
Related Concept Videos
01:34Fluid Mosaic Model
The fluid mosaic model was first proposed as a visual representation of research observations. The model comprises the composition and dynamics of membranes and serves as a foundation for future membrane-related studies. The model depicts the structure of the plasma membrane with a variety of components, which include phospholipids, proteins, and carbohydrates. These integral molecules are loosely bound, defining the cell’s border and providing fluidity for optimal function.LipidsThe most...
01:24Sequence Networks of Rotating Machines
A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
01:21Entropy Changes Accompanying Specific Processes
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
01:23Propagation of Action Potentials
The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
01:58Cooperative Allosteric Transitions
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...