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

Basic Discrete Time Signals01:16

Basic Discrete Time Signals

325
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
325
Exponential and Sinusoidal Signals01:18

Exponential and Sinusoidal Signals

453
The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
453
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

609
The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...
609
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

385
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
385
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

529
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
529
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

413
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
413

You might also read

Related Articles

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

Sort by
Same author

The immune microenvironment: a key regulator of ovarian function during ovarian aging.

Frontiers in immunology·2026
Same author

Universal lateral optical force on an isotropic particle near a dielectric substrate via polarization-induced mirror symmetry breaking.

Optics express·2026
Same author

Lateral optical force on an isotropic dimer induced by high-order multiple scattering under arbitrary polarization states.

Optics express·2026
Same author

Follicular fluid proteomic alterations associated with oocyte developmental potential in polycystic ovary syndrome.

Frontiers in endocrinology·2026
Same author

Causal effects of type 2 diabetes, obesity, gout, and hypothyroidism on carpal tunnel syndrome: a univariable and multivariable Mendelian randomization study.

Korean journal of family medicine·2026
Same author

Homologous Self-Assembled Oligomers as Dual Anode/Cathode Interface Layers for Efficient Organic Photovoltaics.

ACS applied materials & interfaces·2026
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Sep 29, 2025

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.1K

A Fractional-Order Sinusoidal Discrete Map.

Xiaojun Liu1, Dafeng Tang2, Ling Hong3

  • 1School of Sciences, Xi'an University of Posts and Telecommunications, Xi'an 710061, China.

Entropy (Basel, Switzerland)
|March 25, 2022
PubMed
Summary
This summary is machine-generated.

A new fractional-order discrete map exhibits complex nonlinear dynamics like chaos and bifurcations. Increasing the derivative order enhances synchronization speed in these chaotic systems.

Keywords:
a fractional-order discrete mapbifurcationchaossynchronization

More Related Videos

Real-Time Cardiac Mapping with a Noninvasive Imageless Electrocardiographic Imaging System
10:17

Real-Time Cardiac Mapping with a Noninvasive Imageless Electrocardiographic Imaging System

Published on: April 11, 2025

1.0K
Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.8K

Related Experiment Videos

Last Updated: Sep 29, 2025

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.1K
Real-Time Cardiac Mapping with a Noninvasive Imageless Electrocardiographic Imaging System
10:17

Real-Time Cardiac Mapping with a Noninvasive Imageless Electrocardiographic Imaging System

Published on: April 11, 2025

1.0K
Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.8K

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Fractional Calculus

Background:

  • Discrete maps are fundamental in modeling complex systems.
  • Fractional-order systems offer richer dynamics than integer-order counterparts.
  • Understanding bifurcations and chaos is crucial for system control.

Purpose of the Study:

  • To propose and analyze a novel fractional-order discrete map with sinusoidal nonlinearity.
  • To investigate its stability, symmetry, and complex dynamics.
  • To explore bifurcations and achieve heterogeneous hybrid synchronization.

Main Methods:

  • Theoretical analysis for equilibrium points and symmetry.
  • Numerical simulations for dynamics in commensurate and incommensurate orders.
  • Nonlinear tools (bifurcation diagrams, Lyapunov exponents) for analysis.
  • Controller design for synchronization.

Main Results:

  • The map exhibits typical nonlinear features including chaos and various bifurcations (Hopf, period-doubling, symmetry-breaking).
  • Bifurcation analysis in 3D space reveals parameter and order influences.
  • Symmetry-breaking bifurcation points are unaffected by order variations.
  • Heterogeneous hybrid synchronization is successfully achieved.

Conclusions:

  • The proposed fractional-order discrete map demonstrates complex and tunable nonlinear behaviors.
  • Order variation impacts dynamics and synchronization speed, with higher orders accelerating synchronization.
  • The study provides insights into fractional-order chaotic systems and their synchronization.