SPATIAL DYNAMICS WITH HETEROGENEITY

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)S225-S248
JournalSIAM Journal on Applied Mathematics
Volume84
Issue number3
DOIs
StatePublished - 2024

ASJC Scopus subject areas

  • Applied Mathematics

Keywords

  • PDEs
  • brain development
  • ecology
  • integro-differential equations
  • savanna-forest

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