Abstract: | Natural ecosystems often harbor many interacting species, which suggests that they might be amenable to analysis using tools from statistical physics, with high diversity playing the role of the thermodynamic limit. In this limit, dynamical phase-transitions have been found in theoretical models. Here we study one such transition, from a fixed-point phase to a chaotic phase. We analyze the behavior near this continuous transition using a perturbation expansion, and derive a self-consistent equation for the size of the dynamical fluctuations there. We show evidence towards an intriguing conclusion: that this self-consistent equation might not admit a non-trivial solution corresponding to a chaotic phase. |