Order and the ubiquitous occurrence of chaos

A. S. Fokas; T. Bountis

doi:10.1016/0378-4371(95)00435-1

Order and the ubiquitous occurrence of chaos

A. S. Fokas, T. Bountis

Department of Mathematics

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

12 Citations (Scopus)

Abstract

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 t-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 first order ODE's in complex t.

Original language	English
Pages (from-to)	236-244
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	228
Issue number	1-4
DOIs	https://doi.org/10.1016/0378-4371(95)00435-1
Publication status	Published - Jun 15 1996

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

Access to Document

10.1016/0378-4371(95)00435-1

Fingerprint Dive into the research topics of 'Order and the ubiquitous occurrence of chaos'. Together they form a unique fingerprint.

Cite this

@article{c8a54db8a79a4bfe9410293056308a4b,

title = "Order and the ubiquitous occurrence of chaos",

abstract = "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 t-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 first order ODE's in complex t.",

author = "Fokas, {A. S.} and T. Bountis",

year = "1996",

month = jun,

day = "15",

doi = "10.1016/0378-4371(95)00435-1",

language = "English",

volume = "228",

pages = "236--244",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier",

number = "1-4",

}

TY - JOUR

T1 - Order and the ubiquitous occurrence of chaos

AU - Fokas, A. S.

AU - Bountis, T.

PY - 1996/6/15

Y1 - 1996/6/15

N2 - 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 t-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 first order ODE's in complex t.

AB - 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 t-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 first order ODE's in complex t.

UR - http://www.scopus.com/inward/record.url?scp=0030164513&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030164513&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(95)00435-1

DO - 10.1016/0378-4371(95)00435-1

M3 - Article

AN - SCOPUS:0030164513

VL - 228

SP - 236

EP - 244

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-4

ER -