Related Experiment Video
Updated: Oct 26, 2025
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.3K
Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator
V P Kruglov1, D A Krylosova2, I R Sataev1
1Kotelnikov Institute of Radioengineering and Electronics of RAS, Saratov Branch, Zelenaya str. 38, Saratov 410019, Russia.
Chaos (Woodbury, N.Y.)
|August 3, 2021
Summary
This study numerically and experimentally investigates the transition to chaos in systems with quasiperiodic forcing. It reveals chaotic attractors with an additional zero Lyapunov exponent, particularly after torus doubling.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Experimental Physics
Background:
- Transition to chaos is a fundamental concept in nonlinear dynamics.
- Quasiperiodic forcing can lead to complex dynamical behaviors, including chaos.
- Torus destruction is a known route to chaos.
Purpose of the Study:
- To numerically and experimentally study the transition to chaos via torus destruction under quasiperiodic forcing.
- To investigate the properties of chaotic attractors in such systems, specifically the presence of an additional zero Lyapunov exponent.
- To analyze the influence of feedback on chaotic dynamics.
Main Methods:
- Numerical simulations using the Hénon map and Toda oscillator.
- Experimental investigation using a quasi-periodically excited RL-diode circuit.
- Analysis of dynamic regimes, oscillation modes, and Lyapunov exponents, including the effect of feedback.
Main Results:
- Confirmed the transition to chaos via torus doubling in both numerical and experimental models.
- Identified a characteristic feature: chaotic attractors possess an additional zero Lyapunov exponent.
- Demonstrated the impact of feedback, where forcing frequency becomes a dynamic variable.
Conclusions:
- The study confirms a specific route to chaos characterized by torus doubling and an additional zero Lyapunov exponent.
- This finding holds for both numerical models and experimental systems under quasiperiodic forcing.
- Feedback mechanisms can further influence the observed chaotic dynamics.
Related Concept Videos
01:06Forced Oscillations
7.1K
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.
7.1K
01:30Oscillations In An LC Circuit
2.6K
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
2.6K
01:07Damped Oscillations
6.3K
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...
6.3K
01:04Oscillations about an Equilibrium Position
6.1K
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...
6.1K
01:21Simple Harmonic Motion
11.4K
Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator...
11.4K
01:17Characteristics of Simple Harmonic Motion
14.3K
The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...
14.3K