Interesting bifurcations in walking droplet dynamics

Document Type

Article

Publication Date

11-1-2020

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.

Identifier

85086502049 (Scopus)

Publication Title

Communications in Nonlinear Science and Numerical Simulation

External Full Text Location

https://doi.org/10.1016/j.cnsns.2020.105348

ISSN

10075704

Volume

90

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