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

TL;DR

This paper introduces a non-Kolmogorovian framework using soliton rate equations to model population dynamics interacting with environments, revealing phenomena like hibernation and decay blocking.

Contribution

It develops a formalism for soliton rate equations linked to non-Kolmogorovian probability models, with explicit examples involving environment interactions.

Findings

Population decay can be blocked or slowed by environmental coupling.

The formalism models seasonal effects on populations.

Phenomena analogous to hibernation are observed.

Abstract

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.