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

Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.4K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.4K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

212
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,...
212
First Order Systems01:21

First Order Systems

258
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
258
State Space Representation01:27

State Space Representation

388
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...
388
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.0K
Second Order systems II01:18

Second Order systems II

278
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.
278

You might also read

Related Articles

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

Sort by
Same author

Modeling and analyzing glucose-insulin interactions during diabetes through fractional dynamics in presence of glucagon.

Journal of advanced research·2026
Same author

Resurgence in focus: Covid-19 dynamics and optimal control frameworks.

Global epidemiology·2025
Same author

Memory impacts in hepatitis C: A global analysis of a fractional-order model with an effective treatment.

Computer methods and programs in biomedicine·2024
Same author

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors.

International journal of dynamics and control·2023
Same author

A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact.

Healthcare analytics (New York, N.Y.)·2023
Same author

Retraction: "On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems" [Chaos 29, 023111 (2019)].

Chaos (Woodbury, N.Y.)·2022

Related Experiment Video

Updated: Nov 27, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.8K

Modelling of Chaotic Processes with Caputo Fractional Order Derivative.

Kolade M Owolabi1,2, José Francisco Gómez-Aguilar3, G Fernández-Anaya4

  • 1Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

This study explores chaotic dynamical systems by replacing integer-order derivatives with fractional-order ones. Fractional calculus reveals complex species evolution patterns in time and space.

Keywords:
chaotic dynamicschebyshev spectral methodfractional differential equationspatiotemporal oscillationsstability analysis

More Related Videos

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

10.4K

Related Experiment Videos

Last Updated: Nov 27, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.8K
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

10.4K

Area of Science:

  • Dynamical Systems
  • Fractional Calculus
  • Numerical Analysis

Background:

  • Chaotic dynamical systems exhibit complex behaviors.
  • Traditional models often use integer-order derivatives.
  • Fractional calculus offers a more nuanced approach to modeling dynamic processes.

Purpose of the Study:

  • To investigate chaotic dynamical systems using fractional calculus.
  • To replace integer-order time derivatives with Caputo fractional counterparts.
  • To analyze the impact of fractional orders on system dynamics.

Main Methods:

  • Utilized the Caputo fractional derivative definition.
  • Employed a Chebyshev spectral method for numerical approximation.
  • Performed linear stability analysis on the fractional-order systems.

Main Results:

  • Successfully implemented fractional-order derivatives in chaotic models.
  • Obtained a range of chaotic behaviors dependent on fractional orders.
  • Demonstrated the ability of fractional calculus to capture complex species evolution.

Conclusions:

  • Fractional calculus provides a powerful framework for studying chaotic systems.
  • The choice of fractional order significantly influences the system's dynamics.
  • This approach enhances our understanding of spatio-temporal evolution in complex systems.