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

Cyclic Processes And Isolated Systems01:19

Cyclic 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...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Thermodynamic Systems01:06

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of  tea boiling in a kettle. The tea and...
SFG Algebra01:16

SFG Algebra

In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

You might also read

Related Articles

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

Sort by
Same author

Rigorous computation of expansion in one-dimensional dynamics.

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

Analysis of the chaotic itinerancy phenomenon using entropy and clustering.

Physical review. E·2025
Same author

Reservoir computing on manifolds.

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

Persistent homology elucidates hierarchical structures responsible for mechanical properties in covalent amorphous solids.

Nature communications·2025
Same author

Automated identification of the origin of energy loss in nonoriented electrical steel by feature extended Ginzburg-Landau free energy framework.

Scientific reports·2025
Same author

Error evaluation of partial scattering functions obtained from contrast-variation small-angle neutron scattering.

Journal of applied crystallography·2025

Related Experiment Video

Updated: May 15, 2026

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy
07:20

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy

Published on: February 18, 2022

Combinatorial-topological framework for the analysis of global dynamics.

Justin Bush1, Marcio Gameiro, Shaun Harker

  • 1Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA. bushjc@math.rutgers.edu

Chaos (Woodbury, N.Y.)
|January 3, 2013
PubMed
Summary

This study presents a computational framework using graph algorithms and algebraic topology to automatically analyze the global dynamics of complex systems. It enables the creation of databases detailing system behavior across various parameters and phase spaces.

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

Related Experiment Videos

Last Updated: May 15, 2026

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy
07:20

Simultaneous Visualization of the Dynamics of Crosslinked and Single Microtubules In Vitro by TIRF Microscopy

Published on: February 18, 2022

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

Area of Science:

  • Dynamical Systems Theory
  • Computational Mathematics
  • Topology

Background:

  • Conley's topological approach provides a foundation for analyzing dynamical systems.
  • Understanding global dynamics is crucial for predicting system behavior.
  • Existing methods may lack efficiency in handling multi-parameter systems.

Purpose of the Study:

  • To develop an algorithmic framework for automatic computation of global dynamics.
  • To analyze m-parameter semidynamical systems with discrete time.
  • To create a database of system dynamics.

Main Methods:

  • Utilizing efficient graph algorithms.
  • Employing algebraic-topological computational tools.
  • Applying rectangular grids in phase and parameter spaces.

Main Results:

  • An automated framework for computing global dynamics was established.
  • The framework successfully analyzed systems across phase and parameter spaces.
  • Two sample applications demonstrated the framework's utility.

Conclusions:

  • The proposed framework offers an efficient method for dynamical systems analysis.
  • It facilitates the creation of comprehensive dynamics databases.
  • The approach is applicable to complex, multi-parameter systems.