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Order and the ubiquitous occurrence of chaos

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  • Fokas, A.S.
  • Bountis, T.

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.

Suggested Citation

  • Fokas, A.S. & Bountis, T., 1996. "Order and the ubiquitous occurrence of chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 236-244.
  • Handle: RePEc:eee:phsmap:v:228:y:1996:i:1:p:236-244
    DOI: 10.1016/0378-4371(95)00435-1
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