Outputs (4)

Pattern Formation in Mesic Savannas (2023)
Journal Article
Patterson, D., Levin, S., Staver, A. C., & Touboul, J. (2024). Pattern Formation in Mesic Savannas. Bulletin of Mathematical Biology, 86(1), https://doi.org/10.1007/s11538-023-01231-7

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous sol... Read More about Pattern Formation in Mesic Savannas.

Spatial Dynamics with Heterogeneity (2023)
Journal Article
Patterson, D. D., Staver, A. C., Levin, S. A., & Touboul, J. D. (2023). Spatial Dynamics with Heterogeneity. SIAM Journal on Applied Mathematics, S225-S248. https://doi.org/10.1137/22m1509850

Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonli... Read More about Spatial Dynamics with Heterogeneity.

Modeling Immunity to Malaria with an Age-Structured PDE Framework (2023)
Journal Article
Qu, Z., Patterson, D., Childs, L. M., Edholm, C. J., Ponce, J., Prosper, O., & Zhao, L. (2023). Modeling Immunity to Malaria with an Age-Structured PDE Framework. SIAM Journal on Applied Mathematics, 83(3), 1098-1125. https://doi.org/10.1137/21m1464427

Non-equilibrium early-warning signals for critical transitions in ecological systems (2023)
Journal Article
Xu, L., Patterson, D., Levin, S. A., & Wang, J. (2023). Non-equilibrium early-warning signals for critical transitions in ecological systems. Proceedings of the National Academy of Sciences, 120(5), Article e2218663120. https://doi.org/10.1073/pnas.2218663120

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to... Read More about Non-equilibrium early-warning signals for critical transitions in ecological systems.