Modelling homeorhesis by ordinary differential equations

Homeorhesis is a necessary feature of any living system. If a system does not perform homeorhesis, it is nonliving. The present work develops the sufficient conditions for the ODE model to describe homeorhesis and suggests the structure of the model. The proposed homeorhesis model is fairly general. It treats homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on the specific system and specific purposes of this analysis. An example of the specification is the PhasTraM model, the homeorhesis-aware nonlinear reaction–diffusion model for hyperplastic oncogeny in the previous works of the author. The qualitative agreement of the developed homeorhesis model with the living-system experimental results is noted. The work also shows that the basic mathematical models (such as the active-particle generalized kinetic theory) are substantially more important for the living-matter studies than in the case of nonliving matter. A few directions for future research are suggested as well.