Related Experiment Video
Updated: Jun 9, 2025
09:43
Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
Published on: March 20, 2017
9.8K
Synchronization on fractional multiplex higher-order networks
Chenjun Ma1, Weiyuan Ma1, Xiaoqin Wang1
1School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, China.
Chaos (Woodbury, N.Y.)
|October 21, 2024
Summary
This study introduces a fractional multiplex higher-order network model. It demonstrates achieving intra-layer, inter-layer, and complete synchronization using Lyapunov methods and fractional inequalities.
Area of Science:
- Complex Networks
- Nonlinear Dynamics
- Fractional Calculus
Background:
- Multiplex networks involve multiple layers of interactions.
- Higher-order interactions capture group dynamics.
- Synchronization is crucial for network function.
Purpose of the Study:
- To establish a fractional multiplex higher-order network model.
- To investigate synchronization phenomena within this model.
- To analyze intra-layer, inter-layer, and complete synchronization.
Main Methods:
- Development of a fractional multiplex higher-order network model.
- Application of the Lyapunov direct method.
- Utilization of fractional inequalities and a Lyapunov function.
Main Results:
- Demonstration of intra-layer synchronization.
- Proof of inter-layer synchronization.
- Confirmation of complete synchronization in the network.
Conclusions:
- The proposed model successfully achieves various synchronization types.
- Theoretical results are validated by numerical simulations.
- The study contributes to understanding complex network dynamics.
Related Concept Videos
01:25Multimachine Stability
142
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:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
142
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K
01:25Network Function of a Circuit
266
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
266
01:26Transmission-Line Differential Equations
237
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...
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...
237
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
1.2K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.2K
01:13¹H NMR Signal Multiplicity: Splitting Patterns
5.0K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
5.0K