Speaker
Description
We investigate self-organization in stochastic dynamical systems using rigorous and numerical multiscale analysis. At the mesoscale, the model describes conflict resolution between two types of individuals in interconnected domains. Conflicts occur as a Poisson process governed by the mass-action law. Each conflict in a given domain triggers the transfer of one of the interacting individuals to a neighboring domain. This general mechanism arises in a variety of biological settings.
Our main questions are whether the system self-organizes in finite time and how the self-organization time scales with population and system size. We also examine microscopic variants of individual-level interactions underlying the mesoscopic model. We show that, while some microscopic variants give rise to absorbing Markov chains, others unexpectedly do not. Nevertheless, at the macroscale, all variants reduce to an absorbing Markov chain model, which guarantees self-organization in finite time. We derive upper bounds on the self-organization time and identify a non-Markovian microscopic variant that promotes crowd formation, thereby prolonging self-organization. Overall, our study provides a framework for applying absorbing Markov chain theory to self-organization, especially in systems driven by conflict resolution mechanisms.
