Interesting bifurcations in walking droplet dynamics

Aminur Rahman, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We identify two types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points. These bifurcation types - inspired by recent investigations of mathematical models for walking droplet (pilot-wave) phenomena - are introduced and illustrated. Some of the one-parameter bifurcation types are analyzed in detail and extended from the plane to higher-dimensional spaces. A few applications to walking droplet dynamics are analyzed.

Original languageEnglish (US)
Article number105348
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume90
DOIs
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Bifurcations
  • Chaotic strange attractors
  • Discrete dynamical systems
  • Dynamical crises
  • Homoclinic and heteroclinic orbits
  • Invariant sets
  • Pilot-wave models

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