All Outputs (7)

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.

COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex (2021)
Journal Article
Feng, J., Hsu, W., Patterson, D., Tseng, C., Hsing, H., Zhuang, Z., …Chou, S. (2021). COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex. Science Advances, 7(27), Article eabf6808. https://doi.org/10.1126/sciadv.abf6808

Development of cortical regions with precise, sharp, and regular boundaries is essential for physiological function. However, little is known of the mechanisms ensuring these features. Here, we show that determination of the boundary between neocorte... Read More about COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex.

Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach (2021)
Journal Article
Xu, L., Patterson, D., Staver, A. C., Levin, S. A., & Wang, J. (2021). Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach. Proceedings of the National Academy of Sciences, 118(24), Article e2103779118. https://doi.org/10.1073/pnas.2103779118

The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest–savanna model. Savanna and forest states coexist... Read More about Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach.

Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications (2020)
Journal Article
Patterson, D. D., Levin, S. A., Staver, C., & Touboul, J. D. (2020). Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications. SIAM Journal on Applied Dynamical Systems, 19(4), 2682-2719. https://doi.org/10.1137/19m1298329

Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field limit for a g... Read More about Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications.