Sources of uncertainty in deterministic dynamics: an informal overview
Stewart, Ian. (2011) Sources of uncertainty in deterministic dynamics: an informal overview. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.369 (No.1956). pp. 4705-4729. ISSN 1364-503XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1098/rsta.2011.0113
The discovery of chaotic dynamics implies that deterministic systems may not be predictable in any meaningful sense. The best-known source of unpredictability is sensitivity to initial conditions (popularly known as the butterfly effect), in which small errors or disturbances grow exponentially. However, there are many other sources of uncertainty in nonlinear dynamics. We provide an informal overview of some of these, with an emphasis on the underlying geometry in phase space. The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations (popularly known as tipping points) and collisions of chaotic attractors. We briefly discuss possible ways to detect, exploit or mitigate these effects. The paper is intended for non-specialists.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Dynamics, Chaotic behavior in systems, Deterministic chaos, Bifurcation theory|
|Journal or Publication Title:||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publisher:||The Royal Society Publishing|
|Official Date:||13 December 2011|
|Page Range:||pp. 4705-4729|
|Access rights to Published version:||Restricted or Subscription Access|
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