VI Escola de Física Jayme Tiomno



Hosted on GitHub Pages — Theme based on "Midnight", by mattgraham

Ministrante: Prof. Dr. Ricardo Martínez-García (ICTP-SAIFR)

Aulas: YouTube playlist

Horário: 14h às 16h (BRT)

Carga Horária Total: 10h

Idioma: Na primeira aula será decidido o idioma desse curso (português ou inglês), de acordo com a preferência dos alunos presentes.

Syllabus: Biological systems are inherently stochastic and highly nonlinear. With a focus on ecological systems, this course will present a variety of phenomena that may arise in biological systems due to these two properties, ranging from oscillations in the abundance of two interacting populations to the formation of regular patterns in spatially extended systems. Guided by these paradigmatic examples, we will develop the mathematical framework needed to formalize them and discuss how it could be extended to other scenarios.

Prerequisites: Previous knowledge of differential calculus is very needed. Knowing about ODEs and basic probability (what a probability distribution function is, what is a mean, a variance…) would be desirable. There is no prerequisites on the biology side, I’ll guide the course through examples that I will explain in the lectures.

Bibliography: (there might be overlap between the content of some of the chapters).

  • R. Toral, P. Colet., Stochastic Numerical Methods: An Introduction for Students and Scientists. Wiley-Vch (Chapter 8). Free online versions here and here.
  • J.D. Murray., Mathematical Biology I. An Introduction. Springer. Chapters 1, 3, 13 and 11.
  • J.D. Murray., Mathematical Biology II. Spatial Models and Biomedical Applications. Springer. Chapters 2 and 5.
  • S.H. Strogatz., Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering. Chapters 2 and 6.
  • Leah Edelstein-Keshet, Mathematical Models in Biology. SIAM. Chapters 4, 6 and 10.
  • A. Okubo, S.A. Levin., Diffusion and Ecological Problems: Modern Perspectives. Chapters 1 and 2.
  • Otto, S. P. & Day, T. (2011), A biologist's guide to mathematical modeling in ecology and evolution. Princeton University Press. (Primer 3, Chapters 13-15).

Sugested readings: Classical works in which some of the examples that we will study where first introduced or are reviewed.

  • Turing, Alan Mathison., The chemical basis of morphogenesis. Bulletin of mathematical biology 52.1-2 (1990): 153-197.
  • Fisher, Ronald Aylmer., The wave of advance of advantageous genes. Annals of eugenics 7.4 (1937): 355-369.
  • Black, Andrew J., and Alan J. McKane., Stochastic formulation of ecological models and their applications. Trends in Ecology & Evolution 27.6 (2012): 337-345.
  • Codling, Edward A., Michael J. Plank, and Simon Benhamou., Random walk models in biology. Journal of the Royal Society Interface 5.25 (2008): 813-834.