Related Experiment Video
Updated: Jun 16, 2026
10:45
Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
Published on: May 29, 2017
Exponential synchronization of hybrid coupled networks with delayed coupling
1Department of Mathematics, Southeast University, Nanjing, China. wanglihe07@gmail.com
IEEE Transactions on Neural Networks
|February 23, 2010
Summary
This study explores exponential synchronization in coupled networks with hybrid coupling, introducing novel conditions for achieving synchronization despite asymmetric matrices and time delays. The findings reveal that node degrees and coupling matrices significantly impact the synchronized state.
Area of Science:
- Control Theory
- Network Science
- Chaos Theory
Background:
- Coupled network synchronization is crucial for complex systems.
- Time delays and hybrid coupling present significant challenges in synchronization.
- Existing methods often assume symmetric coupling and uniform delays.
Purpose of the Study:
- To investigate exponential synchronization in coupled networks with hybrid coupling (constant and discrete-delay).
- To develop sufficient conditions for synchronization considering asymmetric and non-diagonal coupling matrices.
- To analyze the influence of network topology and internal delays on the synchronized state.
Main Methods:
- Lyapunov functional method for stability analysis.
- Linear Matrix Inequality (LMI) formulation for deriving synchronization conditions.
- Utilizing a chaotic neural network model to demonstrate the proposed criteria.
Main Results:
- Sufficient conditions for exponential synchronization are derived.
- The coupling matrix can be asymmetric or non-diagonal.
- A novel synchronized state, influenced by node degrees and internal coupling matrices, is identified.
Conclusions:
- The proposed method effectively achieves exponential synchronization in complex networks with hybrid coupling and time delays.
- The findings offer new insights into network dynamics and synchronization phenomena.
- The criteria are validated using chaotic neural networks, demonstrating practical applicability.
Related Concept Videos
01:27¹H NMR: Long-Range Coupling
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
01:17Coupled Reactions
Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions.
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions. Cells...
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions. Cells...
01:23Linear time-invariant Systems
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
01:26Transmission-Line Differential Equations
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 the...
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 the...
01:24BIBO stability of continuous and discrete -time systems
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.
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.
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
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 slanted or...
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 slanted or...