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

Signal and System01:26

Signal and System

1.5K
A signal x(t) is a set of data or a time function representing a variable of interest. Signals typically convey information about a phenomenon, such as atmospheric temperature, humidity, human voice, television images, a dog's bark, or birdsongs. More generally, a signal can be a function of more than one independent variable. For instance, images depend on horizontal and vertical positions and can be regarded as two-dimensional signals. However, this text will focus on one-dimensional...
1.5K
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

718
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...
718
SFG Algebra01:16

SFG Algebra

260
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...
260
State Space Representation01:27

State Space Representation

460
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...
460
Classification of Systems-I01:26

Classification of Systems-I

493
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
493
Signal Flow Graphs01:18

Signal Flow Graphs

540
Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...
540

You might also read

Related Articles

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

Sort by
Same author

Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications.

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

Constructing multi-butterfly attractors based on Sprott C system via non-autonomous approaches.

Chaos (Woodbury, N.Y.)·2019
See all related articles

Related Experiment Video

Updated: Dec 19, 2025

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

401

A simple no-equilibrium chaotic system with only one signum function for generating multidirectional variable hidden

Sen Zhang1, Xiaoping Wang1, Zhigang Zeng1

  • 1School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan 430074, China.

Chaos (Woodbury, N.Y.)
|June 4, 2020
PubMed
Summary

This study introduces a novel, simple chaotic system using a single signum function. It exhibits unique hidden chaotic bursting oscillations and demonstrates good randomness for secure communication and image encryption applications.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.5K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.0K

Related Experiment Videos

Last Updated: Dec 19, 2025

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

401
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.5K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.0K

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Existing no-equilibrium chaotic systems often rely on complex nonlinearities like quadratic terms.
  • There is a need for simpler chaotic systems with unique dynamic behaviors.

Purpose of the Study:

  • To propose a novel, simple no-equilibrium chaotic system.
  • To investigate its unique dynamical properties, including hidden attractors and bursting oscillations.
  • To validate its potential for chaos-based applications.

Main Methods:

  • Development of a new chaotic system with a single signum function.
  • Analysis of system dynamics using phase portraits, time series, and bifurcation diagrams.
  • Numerical simulations including Lyapunov exponents and Kaplan-Yorke dimensions.
  • Hardware circuit implementation and experimental validation.
  • Randomness testing using the National Institute of Standards and Technology (NIST) test suite.

Main Results:

  • A simple no-equilibrium chaotic system with a single signum function was successfully proposed.
  • The system exhibits offset boosting and generates hidden attractors in various configurations (1D, 2D, 3D).
  • An uncommon hidden chaotic bursting oscillation was observed and analyzed.
  • Experimental results from a fabricated hardware circuit confirmed numerical simulations.
  • The generated chaotic pseudo-random sequence passed the NIST randomness tests, indicating suitability for applications.

Conclusions:

  • The proposed simple chaotic system offers a unique alternative to existing complex systems.
  • Its ability to generate hidden attractors and chaotic bursting oscillations, coupled with proven randomness, makes it suitable for secure communication and image encryption.