Related Experiment Video
Updated: Jul 3, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Experimental continuation of periodic orbits through a fold.
J Sieber1, A Gonzalez-Buelga, S A Neild
1School of Engineering, University of Aberdeen, Kings College, Aberdeen, AB24 3UE, United Kingdom.
Physical Review Letters
|July 23, 2008
Summary
This study introduces a novel continuation method for tracking periodic orbits in experiments. The technique successfully follows orbits through instabilities using a control-based setup and Newton iterations.
Area of Science:
- Nonlinear Dynamics
- Experimental Physics
Background:
- Periodic orbits are fundamental in understanding dynamical systems.
- Tracking these orbits experimentally, especially through bifurcations, presents significant challenges.
- Existing methods often struggle with unstable periodic orbits.
Purpose of the Study:
- To develop and demonstrate a robust continuation method for tracking periodic orbits in real-time experiments.
- To enable the continuation of periodic orbits through instabilities and bifurcations.
- To validate the method using a canonical nonlinear system.
Main Methods:
- A control-based experimental setup was employed.
- Newton iterations were integrated to ensure convergence.
- The method was applied to a vertically forced pendulum system.
Main Results:
- The continuation method successfully tracked branches of periodic orbits.
- The technique allowed for the continuation of orbits through a fold bifurcation.
- Initially stable rotations were followed into the unstable regime.
Conclusions:
- The presented continuation method is effective for real-time experimental tracking of periodic orbits.
- The approach overcomes limitations in handling unstable periodic orbits and bifurcations.
- This work provides a valuable tool for experimental nonlinear dynamics research.
Related Concept Videos
01:16Properties of Laplace Transform-II
Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
01:04Oscillations about an Equilibrium Position
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 because...
01:16Circular Orbits and Critical Velocity for Satellites
The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial satellites in orbit. One can examine the circular orbit, the simplest kind of orbit, to understand the relationship between the speed and the period of planets and satellites with respect to their positions and the bodies that they orbit.
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...
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...
01:19Cyclic Processes And Isolated Systems
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
01:17Dynamics Of Circular Motion: Applications
Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for...