✦ LIBER ✦

Order and the ubiquitous occurrence of chaos

✍ Scribed by A.S. Fokas; T. Bountis

Book ID: 103896190
Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 525 KB
Volume: 228
Category: Article
ISSN: 0378-4371
DOI: 10.1016/0378-4371(95)00435-1

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✦ Synopsis

For a large class of ODE's, which includes the Van der Pol equation, we determine analytically the asymptotic location of the singularities in the complex r-plane. By integrating these ODE's numerically we show that if the singularities are dense, which is the generic case, the solution is chaotic, in the sense of sensitive dependence on initial conditions. In the exceptional case that the singularities are not dense, the solution exhibits order (taxis). Chaos is ubiquitous even for jfirs/ order ODE's in complex t.

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