Interesting bifurcations in walking droplet dynamics

Aminur Rahman; Denis Blackmore

doi:10.1016/j.cnsns.2020.105348

Interesting bifurcations in walking droplet dynamics

Aminur Rahman, Denis Blackmore

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 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 language	English (US)
Article number	105348
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	90
DOIs	https://doi.org/10.1016/j.cnsns.2020.105348
State	Published - 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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10.1016/j.cnsns.2020.105348

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title = "Interesting bifurcations in walking droplet dynamics",

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.",

keywords = "Bifurcations, Chaotic strange attractors, Discrete dynamical systems, Dynamical crises, Homoclinic and heteroclinic orbits, Invariant sets, Pilot-wave models",

author = "Aminur Rahman and Denis Blackmore",

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year = "2020",

month = nov,

doi = "10.1016/j.cnsns.2020.105348",

language = "English (US)",

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AU - Rahman, Aminur

AU - Blackmore, Denis

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Bifurcations

KW - Chaotic strange attractors

KW - Discrete dynamical systems

KW - Dynamical crises

KW - Homoclinic and heteroclinic orbits

KW - Invariant sets

KW - Pilot-wave models

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DO - 10.1016/j.cnsns.2020.105348

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SN - 1007-5704

VL - 90

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 105348

ER -

Interesting bifurcations in walking droplet dynamics

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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