Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

1.1K
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
1.1K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

391
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,...
391
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

106
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
106
State Function, Exact and Inexact Differentials01:27

State Function, Exact and Inexact Differentials

61
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
61
Path Between Thermodynamics States01:21

Path Between Thermodynamics States

4.8K
Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
4.8K
Modeling with Differential Equations01:25

Modeling with Differential Equations

145
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
145

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Exploring the dynamics of Lotka-Volterra systems: Efficiency, extinction order, and predictive machine learning.

Chaos (Woodbury, N.Y.)·2025
Same author

Inferring bifurcation diagrams with transformers.

Chaos (Woodbury, N.Y.)·2024
Same author

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.

Frontiers in systems biology·2023
Same author

Controlling epidemic extinction using early warning signals.

International journal of dynamics and control·2022
Same author

Characterizing outbreak vulnerability in a stochastic <i>SIS</i> model with an external disease reservoir.

Journal of the Royal Society, Interface·2022
Same author

Knowledge-based learning of nonlinear dynamics and chaos.

Chaos (Woodbury, N.Y.)·2021
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

Chaos (Woodbury, N.Y.)·2026
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Mar 15, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

672

Computing the optimal path in stochastic dynamical systems.

Martha Bauver1, Eric Forgoston1, Lora Billings1

  • 1Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, New Jersey 07043, USA.

Chaos (Woodbury, N.Y.)
|September 3, 2016
PubMed
Summary
This summary is machine-generated.

Finding optimal paths in stochastic systems is crucial for understanding state transitions. This study presents a novel numerical method using finite-time Lyapunov exponents to compute these optimal paths, even in high-dimensional systems.

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K

Related Experiment Videos

Last Updated: Mar 15, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

672
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K

Area of Science:

  • Computational physics
  • Stochastic systems analysis
  • Dynamical systems theory

Background:

  • Stochastic systems often involve transitions between metastable states.
  • Analytic solutions for optimal escape or switching paths are frequently intractable, especially in high dimensions.
  • Numerical methods are essential for computing optimal paths in complex systems.

Purpose of the Study:

  • To develop a constructive numerical methodology for computing optimal paths in stochastic systems.
  • To address the limitations of analytical approaches in high-dimensional and complex systems.
  • To provide a robust computational tool for identifying escape and switching pathways.

Main Methods:

  • Utilizes finite-time Lyapunov exponents for path characterization.
  • Employs statistical selection criteria for robust analysis.
  • Incorporates a Newton-based iterative minimizing scheme for numerical computation.
  • Applies the method to diverse systems ranging from 2D to 6D.

Main Results:

  • The numerical method successfully computes optimal paths in various stochastic systems.
  • Validated against an analytical solution in a 2D system with internal noise.
  • Demonstrated efficacy in a 4D system and a challenging 2D system where other methods failed.
  • Showcased capability in computing paths within a 6D space, highlighting scalability.

Conclusions:

  • The developed methodology provides an effective numerical approach for determining optimal paths in stochastic systems.
  • The method is versatile and applicable across different system dimensions and complexities.
  • This work offers a powerful tool for researchers studying transitions in metastable states and complex dynamical systems.