Understanding critical behaviour through visualization: A walk around the pitchfork

R. Ball

doi:10.1016/S0010-4655(01)00322-8

Understanding critical behaviour through visualization: A walk around the pitchfork

R. Ball^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

4 Citations (Scopus)

Abstract

The visualization of computed three-dimensional bifurcation surfaces of critical points, or limit-point shells was done for bifurcation problems that contained a pitchfork as an organizing centre. Comparison of notionally equivalent problems depicted the determination of the discontinuous behavior in nonlinear dynamical models by other singularities shaping the bifurcation surface. The boundaries of multiplicity were found to be profoundly different in the case of the CSTR problem and its normal form.

Original language	English
Pages (from-to)	71-75
Number of pages	5
Journal	Computer Physics Communications
Volume	142
Issue number	1-3
DOIs	https://doi.org/10.1016/S0010-4655(01)00322-8
Publication status	Published - 15 Dec 2001
Event	Conference on Computational Physics (CCP'2000) - Gold Coast, Qld., Australia Duration: 3 Dec 2000 → 8 Dec 2000

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10.1016/S0010-4655(01)00322-8

Cite this

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title = "Understanding critical behaviour through visualization: A walk around the pitchfork",

abstract = "The visualization of computed three-dimensional bifurcation surfaces of critical points, or limit-point shells was done for bifurcation problems that contained a pitchfork as an organizing centre. Comparison of notionally equivalent problems depicted the determination of the discontinuous behavior in nonlinear dynamical models by other singularities shaping the bifurcation surface. The boundaries of multiplicity were found to be profoundly different in the case of the CSTR problem and its normal form.",

keywords = "Bifurcation theory, Limit-point shell, Pitchfork, Singularity theory",

author = "R. Ball",

year = "2001",

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N2 - The visualization of computed three-dimensional bifurcation surfaces of critical points, or limit-point shells was done for bifurcation problems that contained a pitchfork as an organizing centre. Comparison of notionally equivalent problems depicted the determination of the discontinuous behavior in nonlinear dynamical models by other singularities shaping the bifurcation surface. The boundaries of multiplicity were found to be profoundly different in the case of the CSTR problem and its normal form.

AB - The visualization of computed three-dimensional bifurcation surfaces of critical points, or limit-point shells was done for bifurcation problems that contained a pitchfork as an organizing centre. Comparison of notionally equivalent problems depicted the determination of the discontinuous behavior in nonlinear dynamical models by other singularities shaping the bifurcation surface. The boundaries of multiplicity were found to be profoundly different in the case of the CSTR problem and its normal form.

KW - Bifurcation theory

KW - Limit-point shell

KW - Pitchfork

KW - Singularity theory

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U2 - 10.1016/S0010-4655(01)00322-8

DO - 10.1016/S0010-4655(01)00322-8

M3 - Conference article

SN - 0010-4655

VL - 142

SP - 71

EP - 75

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 1-3

Y2 - 3 December 2000 through 8 December 2000

ER -

Understanding critical behaviour through visualization: A walk around the pitchfork

Abstract

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