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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO 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.
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

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
Linear time-invariant Systems01:23

Linear 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...
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Probabilistic convergence guarantees for type-II pulse-coupled oscillators.

Joel Nishimura1, Eric J Friedman

  • 1Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

This study demonstrates that pulse-coupled oscillators reliably synchronize from random states across various networks with time delays. The findings offer new methods for analyzing oscillator networks and designing synchronization systems.

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Area of Science:

  • Dynamical Systems
  • Network Science
  • Computational Neuroscience

Background:

  • Pulse-coupled oscillators are fundamental in modeling biological systems and engineered networks.
  • Understanding synchronization dynamics, especially with time delays, is crucial for system stability and function.
  • Previous research established local convergence but lacked comprehensive network-wide analysis.

Purpose of the Study:

  • To demonstrate the high-probability convergence of a large class of pulse-coupled oscillators.
  • To analyze convergence on diverse network structures incorporating time delays.
  • To establish rigorous bounds for convergence probabilities based on network properties.

Main Methods:

  • Combining local convergence results with probabilistic network analysis.
  • Utilizing a classification scheme for type-II phase response curves.
  • Developing rigorous lower bounds for convergence probabilities tied to network density.

Main Results:

  • A large class of pulse-coupled oscillators exhibit high-probability convergence from random initial conditions.
  • Convergence is demonstrated across a broad range of network topologies with time delays.
  • Network density is shown to be a key factor in determining convergence probabilities.

Conclusions:

  • The study provides robust analytical methods for pulse-coupled oscillator networks.
  • Insights are offered into the excitation-inhibition balance in biological systems.
  • The findings support the design of decentralized clock synchronization in sensor networks.