TY - JOUR
T1 - Order and the ubiquitous occurrence of chaos
AU - Fokas, A. S.
AU - Bountis, T.
N1 - Funding Information:
We wish to thank L. Drossos and V. Marinakis for carrying out the numerical calculations and providing us with the figures. We also acknowledge that this work was partially supported by a grant from the P.E.N.E.D. program of the Greek Ministry 01 Industry, Research and Technology. This work was also supported by a Human Capital and Mobility grant from the European Union, No. CHRX-CT93-0107.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
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.
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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 -