Spatial Dynamics with Heterogeneity

Patterson, Denis D.; Staver, A. Carla; Levin, Simon A.; Touboul, Jonathan D.

Abstract

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 nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development.

Citation

Patterson, D. D., Staver, A. C., Levin, S. A., & Touboul, J. D. (online). Spatial Dynamics with Heterogeneity. SIAM Journal on Applied Mathematics, 84(3), S225-S248. https://doi.org/10.1137/22m1509850

• Journal Article Type: Article
• Acceptance Date: Mar 14, 2023
• Online Publication Date: Jul 19, 2023
• Deposit Date: Jun 6, 2024
• Journal: SIAM Journal on Applied Mathematics
• Print ISSN: 0036-1399
• Electronic ISSN: 1095-712X
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 84
• Issue: 3
• Pages: S225-S248
• DOI: https://doi.org/10.1137/22m1509850
• Public URL: https://durham-repository.worktribe.com/output/2474758