ArticlePloS one2022
Global structural stability and the role of cooperation in mutualistic systems.
Article in PloS one, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Stability of Ecological Systems: A Theoretical Review.Physics reports · 2024Article
- Structural stability of invasion graphs for Lotka-Volterra systems.Journal of mathematical biology · 2024Article
- Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure.Entropy (Basel, Switzerland) · 2022Article
- What lies underneath: Precise classification of brain states using time-dependent topological structure of dynamics.PLoS computational biology · 2022Article
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3 authors.
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Abstract
Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions.
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