Related Experiment Video
Updated: Nov 20, 2025
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
8.8K
Critical exponents in coupled phase-oscillator models on small-world networks
Ryosuke Yoneda1, Kenji Harada1, Yoshiyuki Y Yamaguchi1
1Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Physical Review. E
|January 20, 2021
Summary
Synchronization transitions in coupled phase-oscillator models reveal a single universality class on small-world networks. This finding simplifies understanding complex synchronization dynamics, regardless of network structure or coupling functions.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Coupled phase-oscillator models exhibit synchronization transitions between nonsynchronized and partially synchronized states.
- These transitions are crucial for understanding emergent collective behavior in various systems.
- Universality classes, defined by critical exponents, characterize the synchronization transition's behavior.
Purpose of the Study:
- To investigate the number of universality classes in synchronization transitions on small-world networks.
- To determine if the infinite universality classes observed in perfect graphs persist in small-world networks.
- To analyze the critical exponent's dependence on network topology and coupling functions.
Main Methods:
- Simulated coupled phase-oscillator models on small-world networks.
- Analyzed the order parameter's dependence on coupling strength to determine critical exponents.
- Varied natural frequency distributions and coupling functions (up to second harmonics).
Main Results:
- Numerical simulations indicate a reduction to a single universality class on small-world networks.
- The critical exponent is shared across different coupling functions and unimodal, symmetric frequency distributions.
- This contrasts with the infinite universality classes found in perfect graph models.
Conclusions:
- Small-world network topology significantly simplifies the universality classes of synchronization transitions.
- A single universality class and shared critical exponent are observed under specific conditions.
- These findings offer a more unified understanding of synchronization phenomena in complex networks.
Related Concept Videos
02:31Phase Transitions
21.7K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
21.7K
01:04Oscillations about an Equilibrium Position
6.3K
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...
6.3K
02:33Exponential Equations for Modeling Growth
70
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
70
01:30Oscillations In An LC Circuit
2.7K
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
2.7K
01:19Cyclic Processes And Isolated Systems
3.2K
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...
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...
3.2K
01:26Transmission-Line Differential Equations
536
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
536