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

Clipper Circuit01:18

Clipper Circuit

949
A clipper circuit is a fundamental wave-shaping device that harnesses the unique properties of diodes to alter and control waveform characteristics. This technology is widely used in electronic devices, especially in television and radar communication systems, where it enhances waveform modulation in both transmitters and receivers.
The operation of a clipper circuit can be exemplified by analyzing a dual-clipper configuration setup that integrates two ideal diodes, each paired with a biasing...
949
Clamper Circuit01:14

Clamper Circuit

1.2K
A clamper circuit, also known as a DC restorer, represents a specialized variant of the rectifier circuit, notable for its method of taking the output across the diode rather than the capacitor. This configuration lends to several distinctive applications, particularly in handling square wave inputs.
Within this circuit, the diode's orientation prompts the capacitor to charge up to the level of the most negative peak of the input signal. Upon reaching this state, the diode ceases to...
1.2K
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

1.6K
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
1.6K
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

3.3K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
3.3K
Simple Harmonic Motion01:21

Simple Harmonic Motion

15.9K
Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...
15.9K
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

2.5K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
2.5K

You might also read

Related Articles

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

Sort by
Same author

Association Between Anticoagulants and Interacting Drugs and Risk of Major Bleeding in Nonvalvular Atrial Fibrillation: Case-Control Study in SIDIAP, Catalonia, Spain.

Clinical therapeutics·2025
Same author

Experimental Observation of the Motion of Ions in a Resonantly Driven Plasma Wakefield Accelerator.

Physical review letters·2025
Same author

Exploring the influence of endometritis diagnostic criteria on uterine involution, milk yield and fertility in dairy cows.

BMC veterinary research·2025
Same author

Filamentation of a relativistic proton bunch in plasma.

Physical review. E·2024
Same author

Hosing of a Long Relativistic Particle Bunch in Plasma.

Physical review letters·2024
Same author

Slow passage through a Hopf-like bifurcation in piecewise linear systems: Application to elliptic bursting.

Chaos (Woodbury, N.Y.)·2023

Related Experiment Video

Updated: Mar 17, 2026

High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition
05:11

High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition

Published on: June 27, 2025

782

Canards in a minimal piecewise-linear square-wave burster.

M Desroches1, S Fernández-García2, M Krupa1

  • 1Inria Sophia-Antipolis Méditerranée Research Centre, MathNeuro Project-Team 2004 route des Lucioles BP 93, 06902 Valbonne Cedex, France.

Chaos (Woodbury, N.Y.)
|August 1, 2016
PubMed
Summary

We created a minimal piecewise-linear approximation of the Hindmarsh-Rose (HR) neuron model to replicate its complex dynamics, including bursting and canard explosions. This simplified model captures essential behaviors of the original HR neuron model.

More Related Videos

A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

8.1K
Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging
06:20

Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging

Published on: April 28, 2022

2.5K

Related Experiment Videos

Last Updated: Mar 17, 2026

High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition
05:11

High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition

Published on: June 27, 2025

782
A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

8.1K
Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging
06:20

Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging

Published on: April 28, 2022

2.5K

Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Mathematical Biology

Background:

  • The Hindmarsh-Rose (HR) model is a crucial mathematical model for simulating neuronal electrical activity.
  • Understanding the complex dynamics, such as square-wave bursting and canard phenomena, is essential for neuroscience.
  • Previous approximations may not fully capture the intricate behaviors of the original HR model.

Purpose of the Study:

  • To construct a minimal piecewise-linear (PWL) approximation of the HR neuron model.
  • To reproduce all essential dynamics of the original HR model, including square-wave bursting and canard explosions.
  • To analyze the role of homoclinic bifurcations in PWL systems for neuronal bursting.

Main Methods:

  • Developing a minimal piecewise-linear approximation of the HR neuron model.
  • Analyzing the fast subsystem for the presence of homoclinic bifurcations.
  • Applying canard theory for piecewise-linear systems to reproduce spike-adding canard explosions.

Main Results:

  • A continuous PWL approximation's fast subsystem cannot exhibit a homoclinic bifurcation necessary for square-wave bursting.
  • Relaxing the continuity of the vector field allows for the homoclinic bifurcation in the fast subsystem.
  • The study successfully reproduces the spike-adding canard explosion feature using PWL canard theory.

Conclusions:

  • A minimal, discontinuous PWL approximation can accurately capture the complex dynamics of the HR neuron model.
  • This simplified model provides insights into the mechanisms underlying neuronal bursting and canard phenomena.
  • The findings contribute to the development of more efficient computational models in neuroscience.