Work

Spatial Dynamics with Heterogeneity

Year: 2023

Type: article

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.

Source: SIAM Journal on Applied Mathematics

DOI: 10.1137/22m1509850

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

Institutions: Princeton University, High Meadows Environmental Institute, Yale University, Brandeis University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Army Research Office

Awards: G1761480223, Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions, Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions, Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions