Mathematics Colloquia and Seminars
Seduced by symmetry: Nonnormality and strict-removal pulse perturbations of ecological communitiesStudent-Run Research Seminar
|Speaker:||Kaela Vogel, UC Davis|
|Start time:||Tue, Nov 19 2019, 12:30PM|
It is now well known that both the network weights and the topological structure of links are important factors in structuring ecological food webs. Due to biological constraints, such as bioenergetics and body size, the weights between predator and prey of these bidigraph networks are asymmetric. This asymmetry has important implications for the eigenvalue-stability of the Jacobian matrices representing food webs and the dynamics of the resulting linearized solution of the original set of ODEs. Due to the nonnormal nature of the eigenbasis, these systems may both be highly sensitive to parameter uncertainty and have long transient growth in response to perturbations that defies the conclusion one would get from looking at the eigenvalues. One important subtly that underlies the study of transients is that the behavior of a system after a perturbation is dependent on the direction of the perturbation, i.e. the system response to increasing the population of one species may be to return quickly to equilibrium, while increasing the population of species may result in transient growth. This talk will cover the counterintuitive behavior of nonnormal matrices and introduce pseudospectra, a method that uses the norm of the resolvent to better characterize the finite-time behavior of nonnormal operators. I will then talk about my current research in investigating what attributes of an ecological network modeled by a system of Lotka-Volterra predator-prey equations are associated with systems that show transient growth to removal of individuals from certain populations on a network.