Studies in the physics of evolution: creation, formation, destruction

TL;DR

This paper explores the dynamics of catalytic systems across various fields, using topological recurrence relations to analyze complex evolution processes, including socio-physics, biodiversity, and opinion formation.

Contribution

It introduces a novel methodology based on topological recurrence relations to analytically study high-dimensional evolution equations in diverse network systems.

Findings

Cascading events can be triggered by small fluctuations, resembling economic evolution.

The methodology allows mathematical treatment of opinion formation models.

Distinct phases of opinion consensus and mixing are identified.

Abstract

The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the pre-existence of specific other elements is a necessary condition. In previous work some of us showed that the dynamics of the catalytic network equation can be understood in terms of topological recurrence relations paving a path towards the analytic tractability of notoriously high dimensional evolution equations. We apply this philosophy to studies in socio-physics, bio-diversity and massive events of creation and destruction in technological and biological networks. Cascading events, triggered by small exogenous fluctuations, lead to dynamics strongly resembling the qualitative picture of Schumpeterian economic evolution. Further we show that this new methodology allows to mathematically treat a variant of the threshold voter-model of opinion formation on networks. For fixed topology we find distinct phases of mixed opinions and consensus.