A heterogenetic theory of living systems

The problem of the dynamics of living systems and their mathematical representation essentially unfolds on two levels. Firstly, the principles of autopoiesis and operational closure describe how a living system produces and maintains itself. Secondly, living phenomena are recognised as historical, involving the evolution of dynamics and spaces of possibility that change over time. Currently, no differential model can incorporate both of these aspects. We propose adopting the differential heterogenesis framework, which enables us to define differential operators that change in space and time, producing event-based and historical dynamics. In this construction, heterogeneous operator assemblages will be constrained by the principles of autopoiesis and operational closure, providing a theoretical framework for event-based and historical living systems. Finally, we provide a specific example of assembly with Gray-Scott kinetic equations, along with numerical simulations and results.