Publications (5)
Extinctions as a vestige of instability: the geometry of stability and feasibility
Stav Marcus, Ari M. Turner, Guy Bunin
Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all sp…
When can few-species models describe dynamics within a complex community?
Stav Marcus, Guy Bunin
Dynamics of species' abundances in ecological communities are often described using models that only account for a few species. It is not clear when and why this would be possible,…
Local and collective transitions in sparsely-interacting ecological communities
Stav Marcus, Ari M. Turner, Guy Bunin
Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sp…
Fixed points of Boolean networks with sparse connections
Stav Marcus, Ari M. Turner, Guy Bunin +1
We study fixed points of cellular automata with sites on random sparse graphs. In the large limit such models are known to exhibit phase transitions, from a ``frozen'' phas…
Local and extensive fluctuations in sparsely-interacting ecological communities
Stav Marcus, Ari M Turner, Guy Bunin
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynam…