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 | |
| Publication status | Published - Jun 15 1996 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Order and the ubiquitous occurrence of chaos. / Fokas, A. S.; Bountis, T.
In: Physica A: Statistical Mechanics and its Applications, Vol. 228, No. 1-4, 15.06.1996, p. 236-244.Research output: Contribution to journal › Article
}
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 -