Related Experiment Video
Updated: Aug 15, 2026
07:42
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Discretization of frequencies in delay coupled oscillators
1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany. yanchuk@wias-berlin.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
We investigated coupled chaotic oscillators with time-delayed coupling. The study found that time delays discretize oscillator frequencies, especially when delays exceed the oscillator
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Coupled oscillator systems
Background:
- Chaotic oscillators exhibit complex, unpredictable behavior.
- Coupling oscillators can lead to synchronized or complex emergent dynamics.
- Time delays in coupling introduce significant challenges in analyzing system behavior.
Purpose of the Study:
- To analyze the dynamical behavior of two mutually coupled chaotic oscillators.
- To investigate the impact of time-delayed coupling on oscillator dynamics.
- To understand the frequency discretization phenomenon in delayed coupled chaotic systems.
Main Methods:
- Numerical simulations of coupled chaotic oscillator models.
- Analysis of system dynamics under varying time delay parameters.
- Frequency spectrum analysis to identify discretization effects.
Main Results:
- Time-delayed coupling leads to the discretization of allowed oscillator frequencies.
- This frequency discretization is prominent when the time delay is significantly larger than the intrinsic period of individual oscillators.
- The study demonstrates a novel effect of time delay on the spectral properties of chaotic systems.
Conclusions:
- Time delay is a critical parameter that fundamentally alters the dynamics and frequency characteristics of coupled chaotic oscillators.
- The observed frequency discretization offers new insights into the behavior of complex delayed systems.
- This research has implications for understanding and controlling chaotic systems in fields with inherent time lags.
Related Concept Videos
01:26Discrete-time Fourier transform
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
One of the notable...
01:31Oscillations 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
01:17Design Example: Underdamped Parallel RLC Circuit
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...
01:20Discrete-Time Fourier Series
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
For a discrete-time periodic signal x[n]...
01:19Limits with Oscillating Discontinuities
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
01:16Basic Discrete Time Signals
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...