Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics

• Probabilistic models used in quantum mechanics apply to contextual problems.
• Any environment defines a context for its subsystems.
• System-environment dynamics can be formulated in a contextual formalism.
• The resulting autocatalytic rate equations can be exactly solved by soliton techniques.
• Several examples are explicitly analyzed.

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.