Related Experiment Video
Updated: Jul 2, 2025
15:58
Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing
Published on: December 3, 2013
5.8K
Delay-induced amplitude death in multiplex oscillator network with frequency-mismatched layers
Keiji Konishi1, Koki Yoshida2, Yoshiki Sugitani1
1Department of Electrical and Electronic Systems Engineering, Osaka Metropolitan University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan.
Physical Review. E
|February 17, 2024
Summary
This study analyzes amplitude death stability in multiplex Stuart-Landau oscillator networks with delayed connections. Commuting network topologies simplify stability analysis, ensuring robust amplitude death even with frequency mismatches.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Amplitude death is a phenomenon in coupled oscillators where oscillations cease.
- Multiplex networks involve multiple layers of interactions.
- Delayed connections can significantly alter network dynamics.
Purpose of the Study:
- To analytically investigate the stability of amplitude death in a multiplex Stuart-Landau oscillator network.
- To explore the impact of delayed interlayer connections on stability.
- To develop conditions for stable amplitude death in such networks.
Main Methods:
- Analytical investigation of the characteristic equation for stability.
- Analysis of network topology matrices and their commutative properties.
- Numerical verification of analytical results.
Main Results:
- Commuting network topology matrices simplify the stability characteristic equation.
- Stability of amplitude death in multiplex networks is comparable or more conservative than in simpler coupled systems.
- A design procedure for stable amplitude death with delayed interlayer connections is provided for commuting matrices.
Conclusions:
- The commutative property of network topology matrices is crucial for simplified stability analysis.
- Stable amplitude death can be achieved in multiplex oscillator networks with appropriate delayed interlayer connections.
- The findings offer insights into controlling dynamics in complex oscillatory networks.
Related Concept Videos
01:17Design Example: Underdamped Parallel RLC Circuit
292
Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
Starting with a fixed...
292
01:30Oscillations In An LC Circuit
2.3K
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
2.3K
01:30RLC Circuit as a Damped Oscillator
986
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
986
01:20Design Example: Capacitance Multiplier Circuit
774
In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
774
01:25Multimachine Stability
153
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:
153
01:16Cascaded Op Amps
633
Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
633