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Details of Grant 

EPSRC Reference: EP/J010820/1
Title: Control-based bifurcation analysis for experiments
Principal Investigator: Sieber, Dr J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Technical University of Denmark
Department: Mathematical Sciences
Organisation: University of Exeter
Scheme: First Grant - Revised 2009
Starts: 01 July 2012 Ends: 30 June 2014 Value (£): 85,003
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
30 Jan 2012 Mathematics Prioritisation Panel Meeting January 2012 Announced
Summary on Grant Application Form
Many phenomena that are predicted to exist by mathematical theory

remain invisible in real life. Yet, mathematical theory also predicts

that these hidden phenomena determine our fate when real life is "on

the edge". For example, a small increase of wind strength can abruptly

cause a bridge cable to start swinging violently. Still more puzzling,

the bridge cable may continue to swing strongly even if the wind

strength decreases again. Mathematical theory reveals that the

mechanisms behind these striking sudden changes (often catastrophes

from the point of view of engineering) are universal: they apply to a

bridge cable as well as to an ocean current or a neuron. The observed

change is abrupt only because the missing link between the two

different visible behaviours is typically a phenomenon that is

unstable or too sensitive to be visible. This insight enables

engineers and scientists to predict, and avoid or control, sudden

changes whenever they can rely on a set of equations describing the


This research will develop a method, "control-based continuation",

that enables experimenters to observe unstable phenomena directly in

controlled laboratory experiments. Control-based continuation uses

control to convert the relation between experimental inputs and

outputs into an equation that can be solved computationally. Every

phenomenon that is natural in the uncontrolled experiment can be found

as a solution of this equation. Mechanical prototype experiments

(using, for example, pendula and beam-magnet arrangements) have shown

that the method is indeed feasible. This project aims to make

control-based continuation applicable to more complex experiments and

more complex phenomena.

The PI will collaborate with experimenters at the Technical University

of Denmark (Lyngby) who investigate vibrations in fast rotating


One specific objective of the project is to develop and test the continuation

of the exact boundaries between stability and instability (so-called

bifurcations). Traditional computational methods for determining

bifurcations are not applicable to equations extracted from

measurements because they rely on the ability to solve the equation

with high accuracy (8-16 significant digits), which is not achievable

in most experiments.

Key Findings
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Potential use in non-academic contexts
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Date Materialised
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Organisation Website: http://www.ex.ac.uk