Analysis of oscillatory plant transpiration

Rhythms in Plants

“…Gumowski 1981Gumowski , 1983. Coupled models have a correspondingly higher number of dynamic variables.…”

“…A nonlinear model with three variables can show period-doubling and chaotic behavior (Strogatz 1994). Complicated, non-sinusoidal waveforms have been encountered experimentally (Johnsson 1976, Johnsson andPrytz 2002) and some efforts to model their shape have been published (Gumowski 1981(Gumowski , 1983. If time delays are introduced in the reactions, the overall model becomes even more apt to show oscillations.…”

Self‐sustained oscillations in plant water regulation: Induction of bifurcations and anomalous rhythmicity

“…In principle, these models should be capable of simulating the complicated dynamics demonstrated experimentally. Although period-2 behaviour can be simulated in variants of some of the models (Gumowski, 1983;Johnsson & Prytz, 2002), period-3 and higher period oscillations have, to date, not been simulated. Chaotic behaviour has not been observed in model simulations but it has been proposed that, in theory, such behaviour is possible (Gumowski, 1983).…”

“…Although period-2 behaviour can be simulated in variants of some of the models (Gumowski, 1983;Johnsson & Prytz, 2002), period-3 and higher period oscillations have, to date, not been simulated. Chaotic behaviour has not been observed in model simulations but it has been proposed that, in theory, such behaviour is possible (Gumowski, 1983). Thus, further model studies should be conducted in order to incorporate these new experimental findings and explore under which conditions they can occur.…”

“…The period doubling encountered in Avena leaves has been the transition from period-1 to period-2 oscillations ( Johnsson & Prytz, 2002). Period doubling has also been found in simulations of a mathematical model of the water regulatory system indicating that, in theory, period doubling can arise in such systems (Gumowski, 1983).…”