Related Experiment Video
Updated: Jun 2, 2026
11:54
Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
Published on: May 8, 2021
Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback.
Pushpita Ghosh1, Shrabani Sen, Syed Shahed Riaz
1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.
Summary
Time-delayed feedback controls nonlinear dynamical systems. This study reveals how delay affects birhythmic van der Pol oscillators, observing collapses and revivals in their behavior.
Area of Science:
- Nonlinear Dynamics
- Control Theory
Background:
- Time-delayed feedback is a key control method for nonlinear dynamical systems.
- Birhythmicity describes systems with two distinct coexisting periodic behaviors.
Purpose of the Study:
- To investigate the influence of time-delayed feedback on the dynamics of a multicycle van der Pol oscillator.
- To analyze the transitions between birhythmic and monorhythmic behaviors under varying delay times.
Main Methods:
- Numerical simulations of the van der Pol oscillator dynamics.
- Analysis using amplitude equations.
Main Results:
- The bifurcation space of the birhythmic system is divided into distinct subspaces based on delay strength.
- Observed collapse and revival of birhythmicity with changes in delay time.
- Demonstrated transitions between birhythmicity and monorhythmicity.
Conclusions:
- Time-delayed feedback significantly alters the dynamical response of birhythmic systems.
- The interplay between delay time and system parameters governs the emergence and disappearance of birhythmicity.
Related Concept Videos
01:07Time-Domain Interpretation of PD Control
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
01:27Time and frequency -Domain Interpretation of PI Control
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
01:21Time and frequency -Domain Interpretation of Phase-lag Control
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
01:24Time and frequency -Domain Interpretation of Phase-lead Control
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
01:23Root Loci for Positive-Feedback Systems
The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
The construction rules for the root locus in positive feedback systems are similar to those in...
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...