  Soliton rate equations are based on non-Kolmogorovian models of probability
and naturally include autocatalytic processes. The formalism is not widely
known but has great unexplored potential for applications to systems
interacting with environments. Beginning with links of contextuality to
non-Kolmogorovity we introduce the general formalism of soliton rate equations
and work out explicit examples of subsystems interacting with environments. Of
particular interest is the case of a soliton autocatalytic rate equation
coupled to a linear conservative environment, a formal way of expressing
seasonal changes. Depending on strength of the system-environment coupling we
observe phenomena analogous to hibernation or even complete blocking of decay
of a population.
