Related Experiment Video
Updated: May 6, 2026
14:18
Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
Published on: February 28, 2016
11.0K
Time delay induced stochastic dynamics in a strongly nonlinear energy harvesting system
Yanxia Zhang1, Shaoyi Shi1, Yanfei Jin2
1School of Sciences, Xi'an University of Science and Technology, Xi'an 710054, Shaanxi, China.
Chaos (Woodbury, N.Y.)
|May 5, 2026
Summary
Time delays significantly impact nonlinear energy harvesting systems, even at small values. An extended stochastic averaging method reveals how time delays and feedback control influence system dynamics and performance.
Area of Science:
- Nonlinear dynamics
- Energy harvesting systems
- Stochastic processes
Background:
- Practical energy harvesting systems exhibit complex dynamics due to time delays, environmental noise, and inherent nonlinearities.
- Existing theoretical methods struggle to accurately model these complex, time-delayed stochastic systems.
- New analytical approaches are needed to understand and optimize system performance under realistic conditions.
Purpose of the Study:
- To investigate the stochastic dynamics of a strongly nonlinear energy harvesting system with time delay.
- To develop and apply an extended stochastic averaging method for analyzing time-delayed systems.
- To determine the influence of time delay parameters on system response and mean output power.
Main Methods:
- An extended stochastic averaging method of energy envelope was developed.
- Analytical expressions for stationary probability density and mean output power were derived.
- Monte Carlo numerical simulations were used for verification.
Main Results:
- Time delays, even small ones, significantly affect the dynamic characteristics of energy harvesting systems.
- Both time-delayed feedback gain and the delay duration influence system performance.
- Appropriate time-delayed feedback control can substantially enhance system performance.
Conclusions:
- The extended stochastic averaging method effectively analyzes time-delayed nonlinear systems.
- Time delays are critical factors in energy harvesting system design and performance.
- Optimizing time-delayed feedback control is a promising strategy for improving energy harvesting efficiency.
More Related Videos
Related Concept Videos
01:07Damped Oscillations
6.2K
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...
6.2K
01:23Energy in Simple Harmonic Motion
8.9K
To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...
8.9K
01:18Second Order systems II
559
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
559
01:06Forced Oscillations
6.3K
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.
6.3K
01:21Linear Approximation in Time Domain
460
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
460
01:17Problem Solving: Energy in Simple Harmonic Motion
2.2K
Simple harmonic motion (SHM) is a type of periodic motion in time and position, in which an object oscillates back and forth around an equilibrium position with a constant amplitude and frequency. In SHM, there is a continuous exchange between the potential and kinetic energy, which results in the oscillation of the object.
Consider the spring in a shock absorber of a car. The spring attached to the wheel executes simple harmonic motion while the car is moving on a bumpy road. The force on the...
Consider the spring in a shock absorber of a car. The spring attached to the wheel executes simple harmonic motion while the car is moving on a bumpy road. The force on the...
2.2K