New perspectives: stability and complex dynamics of food webs via Hamiltonian methods

TL;DR

This paper explores how Hamiltonian methods can be used to analyze the stability and complex dynamics of large ecological food webs, revealing the influence of network topology and interaction structure on ecological stability.

Contribution

It introduces a novel application of Hamiltonian methods to ecological networks, linking network topology with stability and biodiversity.

Findings

Hamiltonian structure promotes stability and biodiversity

Strongly connected nodes influence network dynamics

Catastrophic shifts depend on ecological interaction patterns

Abstract

We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely, existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and investigate how these phenomena depend on ecological interaction structure. We show that a Hamiltonian structure of interaction leads to stability and large biodiversity.