Gonzalo Robledo - Sensitivity analysis for time varying ecological networks скачать в хорошем качестве

Gonzalo Robledo - Sensitivity analysis for time varying ecological networks

Theoretical Ecology Seminar from the IITE (https://iite.info) by Gonzalo Robledo (Universidad de Chile). Recorded 4th Nov 2025. Abstract: We propose a generalization of the sensitivity analysis to press perturbations for ecological networks described by time-varying ODE systems. Sensitivity analysis is a classical tool which has been successfully employed to assess the overall effects stemming from sustained changes in species growth rates on the equilibrium values of other indirectly related species in time invariant networks. Nevertheless, its generalization to the time varying case has remained elusive. Our generalization is based in two classical ODE topics: i) the smoothness of solutions of with respect to parameters and ii) the properties of exponential dichotomy and admissibility, which were combined with recent advances in the theory of non autonomous dynamical systems inspired by the new concept of non autonomous equilibrium and its local properties. We derive the sensitivity matrix as the solution of a non-homogeneous linear matrix differential equation, which can be explicitly computed using results from exponential dichotomy and admissibility. In addition, time averaging provides alternative characterizations for the sensitivity matrix in terms of the community matrix. In collaboration with Rodrigo Ramos-Jiliberto (Universidad Mayor, Chile) and Daniel Sepúlveda (Universidad Tecnológica Metropolitana, Chile).