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

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

843
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....
843
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

900
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
900
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

334
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
334
Classification of Systems-II01:31

Classification of Systems-II

430
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,
430
Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

2.8K
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
2.8K
Second Order systems II01:18

Second Order systems II

338
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.
338

You might also read

Related Articles

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

Sort by
Same author

Symmetry kills the square in a multifunctional reservoir computer.

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

Multifunctionality in a reservoir computer.

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

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

Chaos (Woodbury, N.Y.)·2026
Same journal

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

Chaos (Woodbury, N.Y.)·2026
Same journal

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

Chaos (Woodbury, N.Y.)·2026
Same journal

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Dec 27, 2025

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.5K

Border-collision bifurcations in a driven time-delay system.

Pierce Ryan1, Andrew Keane1, Andreas Amann1

  • 1School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland.

Chaos (Woodbury, N.Y.)
|March 2, 2020
PubMed
Summary
This summary is machine-generated.

A simple mathematical model with time delay and periodic forcing exhibits complex dynamics, including torus bifurcations and multistability. These behaviors are analytically explained using border-collision bifurcations in the Poincaré map.

More Related Videos

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

20.8K
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.4K

Related Experiment Videos

Last Updated: Dec 27, 2025

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.5K
Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

20.8K
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.4K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics
  • Mathematical Modeling

Background:

  • Time delays and periodic forcing are prevalent in many real-world systems.
  • Understanding complex dynamics in simple models offers broad applicability.
  • Piecewise-linear systems provide a tractable framework for analyzing nonlinear phenomena.

Purpose of the Study:

  • To investigate the bifurcation structure of a simple piecewise-linear system with time delay and periodic forcing.
  • To analytically explain the observed dynamical features, including torus bifurcations and multistability.
  • To provide widely applicable insights into systems with time delay and periodic forcing.

Main Methods:

  • Analysis of a piecewise-linear system incorporating time delay and periodic forcing.
  • Identification and characterization of torus bifurcations and Arnold tongues.
  • Application of border-collision bifurcation theory to an associated Poincaré map.

Main Results:

  • A rich bifurcation structure, including torus bifurcations and Arnold tongues, was observed.
  • Multistability was found to exist across a significant portion of the parameter space.
  • The complex dynamics were successfully explained via border-collision bifurcations of the Poincaré map.

Conclusions:

  • Simple systems with time delay and periodic forcing can generate complex dynamics.
  • Analytical methods, particularly border-collision bifurcations, are effective for understanding these dynamics.
  • The findings offer valuable insights for modeling diverse scientific and engineering problems.