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 Order systems II01:18

Second Order systems II

93
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.
93
Second Order systems I01:20

Second Order systems I

139
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
139
Classification of Systems-II01:31

Classification of Systems-II

137
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
137
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

470
In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
470
Damped Oscillations01:07

Damped Oscillations

5.7K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
5.7K
First Order Systems01:21

First Order Systems

87
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...
87

You might also read

Related Articles

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

Sort by
Same author

The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation.

Entropy (Basel, Switzerland)·2023
Same author

Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook.

Sensors (Basel, Switzerland)·2023
Same author

Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives.

Entropy (Basel, Switzerland)·2022
Same author

Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case.

Entropy (Basel, Switzerland)·2021
Same author

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements.

Entropy (Basel, Switzerland)·2020
Same author

Strange Attractors Generated by Multiple-Valued Static Memory Cell with Polynomial Approximation of Resonant Tunneling Diodes.

Entropy (Basel, Switzerland)·2020

Related Experiment Video

Updated: Jun 13, 2025

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

11.7K

Chaotic systems based on higher-order oscillatory equations.

Jiri Petrzela1,2

  • 1Department of Radio Electronics, Brno University of Technology, Brno, 61600, Czech Republic. petrzela@vut.cz.

Scientific Reports
|September 10, 2024
PubMed
Summary

Researchers designed novel lumped chaotic systems using higher-order ordinary differential equations. Robust chaos was confirmed in third-order oscillators and a fourth-order system involving superinductor-supercapacitor interactions, validating theoretical and practical findings.

More Related Videos

Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.1K
A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
08:06

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis

Published on: March 19, 2021

2.8K

Related Experiment Videos

Last Updated: Jun 13, 2025

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

11.7K
Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.1K
A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
08:06

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis

Published on: March 19, 2021

2.8K

Area of Science:

  • Chaos Theory
  • Nonlinear Dynamics
  • Electrical Engineering

Background:

  • Higher-order ordinary differential equations describe ideal oscillators.
  • Lumped chaotic systems are crucial for understanding complex nonlinear phenomena.

Purpose of the Study:

  • To design and investigate new lumped chaotic systems.
  • To demonstrate the existence and robustness of chaos in novel oscillator designs.

Main Methods:

  • Construction of third-order chaotic oscillators.
  • Analysis of a fourth-order oscillatory equation based on superinductor-supercapacitor interaction.
  • Numerical analysis including Lyapunov exponents, recurrence plots, approximate entropy, and sensitivity calculations.
  • Practical measurements to verify theoretical predictions.

Main Results:

  • Two dual third-order chaotic oscillators were successfully constructed.
  • Robust chaos was experimentally and numerically verified for both third-order and fourth-order systems.
  • The fourth-order system demonstrated passive nonlinearity essential for chaos evolution.
  • Complex motion was confirmed as robust, not transient or numerical artifacts.

Conclusions:

  • Theoretical assumptions align well with practical results for the designed chaotic systems.
  • The study validates the design principles for lumped chaotic oscillators.
  • Novel chaotic systems with robust chaotic behavior were successfully developed and verified.