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 Experiment Videos

Parametrically forced pattern formation.

Dieter Armbruster1, Marguerite George, Iuliana Oprea

  • 1Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary
This summary is machine-generated.

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

Complex Fluids in a Multifractal Space: Scale Covariance and the Emergence of the Fractal Force.

Entropy (Basel, Switzerland)·2026
Same author

Predictable topological sensitivity of Turing patterns on graphs.

Physical review. E·2022
Same author

A graphical approach to estimate the critical coupling strength for Kuramoto networks.

Chaos (Woodbury, N.Y.)·2019
Same author

Node Survival in Networks under Correlated Attacks.

PloS one·2015
Same author

Three level signal transduction cascades lead to reliably timed switches.

Journal of theoretical biology·2014
Same author

Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology.

Neural networks : the official journal of the International Neural Network Society·2013
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

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

State estimation in spatiotemporal chaos via low-rank StatFEM.

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

Universal response functions in driven dissipative tunneling dynamics.

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

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

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

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

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

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

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

Pattern formation in nonlinear damped Mathieu-type equations is analyzed. Parametric resonance creates patterns, with spatial solitons observed in this dissipative system, offering insights into granular media experiments.

Area of Science:

  • Nonlinear Dynamics
  • Partial Differential Equations
  • Pattern Formation

Background:

  • Analyzing pattern formation in nonlinear damped Mathieu-type partial differential equations.
  • Understanding the influence of parametric resonance on spatial structures.

Purpose of the Study:

  • To perform a bifurcation analysis of an averaged equation and compare it with numerical simulations.
  • To investigate the evolution of patterns with increasing forcing amplitude.

Main Methods:

  • Bifurcation analysis of an averaged equation.
  • Full numerical simulations.
  • Comparison with experimental data from vertically vibrating granular media.

Main Results:

Related Experiment Videos

  • Parametric resonance generates periodically varying patterns influenced by forcing amplitude and detuning.
  • Subcritical pattern onset and attractor crowding observed for large detuning.
  • Spatially homogeneous, temporally periodic solutions emerge at a specific forcing amplitude.
  • Dissipative spatial solitons, representing phase-jump domain walls, are identified.

    • Conclusions:

    • The study elucidates pattern formation mechanisms in a nonlinear damped Mathieu-type PDE.
    • Findings provide a theoretical framework for understanding phenomena in granular media.
    • The existence of spatial solitons in a dissipative system is a significant observation.