Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Search research articles

Related Experiment Videos

Wave propagation in discrete media.

Arnaud Tonnelier¹

¹Techniques de l'Imagerie, de la Modélisation et de la Cognition, CNRS UMR 5525, Faculty of Medicine, La Tronche, France. Arnaudd.Tonnelier@imag.fr

Journal of Mathematical Biology

|April 11, 2002

Summary

This study analyzes nonlinear ordinary differential equations in excitable cell networks, revealing conditions for activity propagation and the behavior of traveling waves. Findings include the existence of waves with distinct front and wake velocities.

Related Concept Videos

You might also read

Related Articles

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

Sort by

Same author

Exact solutions for signal propagation along an excitable transmission line.

Physical review. E·2024

Same author

Threshold curve for the excitability of bidimensional spiking neurons.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014

Same author

Cyclic negative feedback systems: what is the chance of oscillation?

Bulletin of mathematical biology·2014

Same author

Screening of chemicals for human bioaccumulative potential with a physiologically based toxicokinetic model.

Archives of toxicology·2011

Same author

On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks.

Neural computation·2011

Same author

Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation.

Cognitive neurodynamics·2008

Area of Science:

Computational Neuroscience
Mathematical Biology
Nonlinear Dynamics

Background:

Excitable cell networks are fundamental to biological signaling.
Understanding activity propagation is key to modeling biological systems.
Nonlinear ordinary differential equations (ODEs) provide a framework for these models.

Purpose of the Study:

To analyze infinite systems of nonlinear ODEs in one-dimensional lattices of excitable cells.
To determine the conditions for the existence and stability of traveling wave solutions.
To investigate the propagation dynamics, including front and wake velocities.

Main Methods:

Analysis of infinite systems of nonlinear ODEs.
Derivation of conditions for activity propagation speed.
Study of traveling wave solutions' existence and stability.
Generalization to inhomogeneous media and long-range connections.

Main Results:

Calculated the speed of activity propagation for ideal nonlinearities.
Derived the condition for the existence of such propagation.
Established the existence and stability of traveling wave solutions, providing an explicit expression in the simplest case.
Observed unstable traveling waves leading to propagation with distinct front and wake velocities.
Extended findings to inhomogeneous media and networks with long-range connections.

Conclusions:

The study provides a mathematical framework for understanding activity propagation in excitable networks.
Traveling wave solutions exhibit complex dynamics, including distinct front and wake velocities.
The findings are generalizable, offering insights into more complex biological systems.

Related Experiment Videos