We study nonlinear, spatially extended complex systems with a current focus on ecosystems. Nonlinearity allows for instabilities and transitions from one system state to another, the spatial extent allows for a large number of system constituents, and complexity generally implies a hierarchy of organization levels. Large numbers of constituents do not necessarily imply more of the same, as more can be different. A fascinating example is pattern formation (top figures) – a large-scale emergent property induced by small-scale positive feedbacks.
A major objective in understanding complex ecosystems is upscaling information at small spatial scales and low organization levels to system behaviors at large scales and high organization levels. We do that by mathematical modeling and model studies, focusing on the roles pattern formation play in the response of complex ecosystems to varying environments. Pattern formation theory is essential for studying spatial ecology, but the relationship between the two research fields is reciprocal; not only can spatial ecology benefit from the concepts and tools of pattern formation theory, it can also pose new interesting questions in pattern-formation research, with possible applications to other fields of science. This motivates another significant part of our group activities.
More on pattern formation in an upcoming conference on Advances in Pattern Formation: New Questions Motivated by Applications, February 18-21, 2019, Sede Boqer (download poster).