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.
|Number of pages||9|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - Jun 15 1996|
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics