Adding connections can hinder network synchronization of time-delayed oscillators.
Joseph D Hart1,2, Jan Philipp Pade3, Tiago Pereira4,5
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
Summary
Adding network links can surprisingly hinder synchronization in time-delayed systems. This study reveals how connectivity changes and time delays critically impact network synchronization, especially in directed networks.
Area of Science:
- Complex networks
- Nonlinear dynamics
- Synchronization phenomena
Background:
- Network structure significantly influences system dynamics.
- Synchronization is crucial for many complex systems.
- Understanding how connectivity affects synchronization is an ongoing challenge.
Purpose of the Study:
- To investigate the impact of network connectivity modifications on synchronization.
- To identify conditions under which adding links can impair synchronization.
- To explore the role of time delays in network synchronization.
Main Methods:
- Experimental analysis of time-delayed optoelectronic oscillator networks.
- Theoretical analysis using the master stability function approach.
- Comparison of synchronization in directed and undirected networks.
Main Results:
- Adding links to a network can lead to a loss of identical synchronization.
- This counterintuitive effect is dependent on network connectivity and time delays.
- Time delays play a critical role, particularly in larger, directed networks.
Conclusions:
- Network structure modifications must consider time delays to maintain synchronization.
- Directed networks are more susceptible to synchronization loss with increased connectivity.
- Findings offer insights for designing and controlling synchronization in real-world networks.
Related Concept Videos
01:06Forced Oscillations
8.2K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
8.2K
01:21Time and frequency -Domain Interpretation of Phase-lag Control
447
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
447
01:30Oscillations In An LC Circuit
3.4K
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
3.4K
01:04Oscillations about an Equilibrium Position
7.3K
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...
7.3K
01:30RLC Circuit as a Damped Oscillator
2.6K
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...
2.6K
01:23Linear time-invariant Systems
1.1K
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...
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...
1.1K