Recent progress in nonlinear dynamics with applications in critical transitions and evolutionary game theory
Abstract: In this talk I wish to showcase four recent research projects I had the pleasure of being part of, that nicely bring together a variety of topics while sharing the same core: nonlinear dynamics and the acclaimed software DynamicalSystems.jl. In the first half of the talk I will highlight research on extending the very definition of “stability” in dynamical systems, and how this translates to defining, and anticipating, critical transitions. The second half of the talk will explore the role of deterministic chaos underpinning evolutionary game theory. It has been a long-standing debate whether population fluctuations are primarily the result of deterministic chaos, or they are just a product of noise. Our research illustrated how using complexity measures one can identify signatures of deterministic chaos in purely stochastic evolutionary models.