Related Experiment Video
Updated: Mar 29, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.8K
Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch.
A N Pisarchik1,2, R Jaimes-Reátegui2,3
1Centro de Investigaciones en Optica, Loma del Bosque 115, 37150 Leon, Guanajuato, Mexico.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
A small frequency mismatch in coupled chaotic oscillators can surprisingly enhance regularity in the slave system. This "chaos by chaos" stabilization effect improves signal coherence through specific Lyapunov exponent changes.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Coupled chaotic oscillators are fundamental in nonlinear dynamics.
- Unidirectional coupling can lead to complex emergent behaviors.
- Frequency mismatch effects in chaotic systems are not fully understood.
Purpose of the Study:
- To investigate the phenomenon of coherence resonance in unidirectionally coupled chaotic oscillators.
- To explore the role of natural frequency mismatch in inducing regularity.
- To analyze the underlying mechanisms of "stabilization of chaos by chaos."
Main Methods:
- Utilized unidirectionally coupled chaotic oscillators.
- Systematically varied the natural frequency mismatch between master and slave oscillators.
- Quantified coherence using power spectrum analysis, amplitude and interval statistics, and Lyapunov exponents.
Main Results:
- A small natural frequency mismatch induced coherence resonance in the slave oscillator.
- This phenomenon was termed "stabilization of chaos by chaos."
- Enhanced coherence correlated with negative third and fourth Lyapunov exponents.
Conclusions:
- Natural frequency mismatch is a critical parameter for inducing coherence resonance.
- The observed phenomenon demonstrates a novel form of chaos control.
- Lyapunov exponent analysis provides insight into the underlying dynamics of enhanced coherence.
Related Concept Videos
01:19Concept of Resonance and its Characteristics
6.9K
If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not...
6.9K
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
01:30Oscillations 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
01:07Damped Oscillations
7.6K
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.
Although friction and other non-conservative...
Although friction and other non-conservative...
7.6K
01:17Design Example: Underdamped Parallel RLC Circuit
767
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...
767
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