PERIOD LENGTHENING NEAR THE END OF OSCILLATIONS IN CHEMICAL-SYSTEMS

In many oscillating systems, the period of oscillations rises sharply with the change of the control parameter just before the oscillations end, and the system collapses to a stable steady state. This increase in period is usually interpreted as an approach to a homoclinic orbit, in which the period will be in fact infinite. In this paper a few oscillating chemical models are examined near the "end of oscillations". It is found that, although some models do show the period lengthening appropriate for an approach to a homoclinic orbit, others show a much sharper increase, indicating that other period lengthening mechanisms may be operating. The period lengthening may, in some cases, be very dramatic, and periods of up to ∼105 s have been calculated. The experimental and computational implications of such long periods are discussed. © 1990 American Chemical Society.