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

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

64
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
64
Second Order systems II01:18

Second Order systems II

90
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.
90
Second Order systems I01:20

Second Order systems I

136
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...
136
Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

254
In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
254
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

85
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
85
Multi-Step Reactions02:31

Multi-Step Reactions

7.3K
Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
7.3K

You might also read

Related Articles

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

Sort by
Same author

Resident-invader dynamics of similar strategies in fluctuating environments.

Journal of mathematical biology·2020
See all related articles

Related Experiment Video

Updated: Jun 8, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Pulses in singularly perturbed reaction-diffusion systems with slowly mixed nonlinearity.

Yuanxian Chen1, Yuhua Cai1,2, Jianhe Shen1,2

  • 1College of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, Fujian, People's Republic of China.

Chaos (Woodbury, N.Y.)
|November 1, 2024
PubMed
Summary

This study investigates pulse solutions in reaction-diffusion systems with mixed nonlinearity. The single-pulse solution can be stable, while the double-hump solution is always unstable.

More Related Videos

Dissolution Dynamic Nuclear Polarization Instrumentation for Real-time Enzymatic Reaction Rate Measurements by NMR
10:54

Dissolution Dynamic Nuclear Polarization Instrumentation for Real-time Enzymatic Reaction Rate Measurements by NMR

Published on: February 23, 2016

10.6K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.8K

Related Experiment Videos

Last Updated: Jun 8, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K
Dissolution Dynamic Nuclear Polarization Instrumentation for Real-time Enzymatic Reaction Rate Measurements by NMR
10:54

Dissolution Dynamic Nuclear Polarization Instrumentation for Real-time Enzymatic Reaction Rate Measurements by NMR

Published on: February 23, 2016

10.6K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.8K

Area of Science:

  • Mathematical modeling
  • Nonlinear dynamics
  • Reaction-diffusion systems

Background:

  • Reaction-diffusion systems are crucial for modeling phenomena across various scientific disciplines.
  • Singularly perturbed systems present unique challenges in analyzing solution stability.
  • Slowly mixed nonlinearities, generated by trigonometric and power functions, add complexity to pulse dynamics.

Purpose of the Study:

  • To investigate the existence and spectral stability of pulse solutions in singularly perturbed two-component reaction-diffusion systems.
  • To analyze pulse behavior in the presence of a specific type of slowly mixed nonlinearity.
  • To determine conditions for the stability of different pulse types.

Main Methods:

  • Application of geometric singular perturbation theory to establish the existence of single-pulse and double-hump solutions.
  • Development of a novel analytical approach using hypergeometric functions and a comparison theorem to overcome stability analysis challenges.
  • Utilizing the nonlocal eigenvalue problem method to determine slow-fast eigenvalues.

Main Results:

  • Demonstrated the existence of both single-pulse and double-hump solutions within the model.
  • Proved that the double-hump solution is inherently unstable.
  • Established that the single-pulse solution can exhibit stability contingent upon specific parameter values.

Conclusions:

  • The study successfully characterizes pulse solutions in complex reaction-diffusion systems.
  • The findings highlight the critical role of nonlinearity in determining pulse stability.
  • This work provides a robust framework for analyzing stability in systems with challenging nonlinearities.