This lecture, given by Rudolf Hanel, is an online discussion organised under the Scaling in Complex Systems lecture series by Utrecht University. Due to the coronavirus pandemic, the lecture will take place online.
The 45-min lecture is followed by a 45-min Question & Answer session.
Emergent features of steadily driven non-equilibrium processes (e.g. cells, ecosystems, etc.) are not mutually independent. At coarse grained levels of description they can often be understood as regulatory networks that represent systems of typically non-linear dependencies. Ignorance on details of complex regulatory systems typically prevents us to fully specify such networks and reduces the direct predictive value of such models, particularly if some system components are themselves `anticipating subprocess’. However, even simple models can still generically inform us about dynamical properties we may expect from sufficiently large heterogenous regulatory networks.
We use a most primitive `almost linear’ network model suffices to gain insight into how considered state variables, such as the abundance or activity of system features, all non-negative quantities, implement non-linear constraints on the system, causing it to exhibit large numbers of attractors corresponding to limit cycles or fixed points, and with some noise added, multi-stable dynamics (i.e. punctuated equilibria) can be observed.
More interestingly, there exits an extended range in the parameter-space of such systems where the system is very likely to operate `sustainably’ in a stable, or meta-stable way. Outside this range the system almost certainly becomes unstable (fully chaotic or exponential runaway dynamics). If we postulate that the overall stability of regulatory systems plays a role in systemic selection, or the evolution of system parameters, such models may explain emergent modularity and maybe also predominance of suppression mechanisms in regulatory systems as they increase in their diversity of features.