  It is shown that rapid substantial changes in heating rate can induce
transitions to improved energy confinement regimes in zero-dimensional models
for tokamak plasma phenomenology. We examine for the first time the effect of
step changes in heating rate in the models of E-J.Kim and P.H.Diamond,
Phys.Rev.Lett. 90, 185006 (2003) and M.A.Malkov and P.H.Diamond, Phys.Plasmas
16, 012504 (2009) which nonlinearly couple the evolving temperature gradient,
micro-turbulence and a mesoscale flow; and in the extension of H.Zhu,
S.C.Chapman and R.O.Dendy, Phys.Plasmas 20, 042302 (2013), which couples to a
second mesoscale flow component. The temperature gradient rises, as does the
confinement time defined by analogy with the fusion context, while
micro-turbulence is suppressed. This outcome is robust against variation of
heating rise time and against introduction of an additional variable into the
model. It is also demonstrated that oscillating changes in heating rate can
drive the level of micro-turbulence through a period-doubling path to chaos,
where the amplitude of the oscillatory component of the heating rate is the
control parameter.
