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Population Dynamics and nonlinearity
- Population dynamics: an interactive phase diagram
- Interactive iterated map with corresponding time sequence
- Mapa iterativa y su secuencia en tiempo.
- Mapa iterado ajustable e interactivo con secuencia en tiempo
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Population Dynamics and nonlinearity
JimSmithInChiapas, May 31, 2014
A collection of diagrams to help students visualize population dynamics. To help them visualize nonlinearity in general, see the collections Iterated Maps for Middle Schoolers (and beyond) http://www.geogebratube.org/material/show/id/72506 Mapas Iterados: No-linealidad y trayectorias de puntos http://www.geogebratube.org/material/show/id/72276
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1. Population dynamics: an interactive phase diagram
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2. Interactive iterated map with corresponding time sequence
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3. Mapa iterativa y su secuencia en tiempo.
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4. Mapa iterado ajustable e interactivo con secuencia en tiempo
Population dynamics: an interactive phase diagram
A phase diagram of population dynamics, prepared at the request of students who needed to understand the diagrams presented in "Consequential classes of resources: Subtle global bifurcation with dramatic ecological consequences in a simple population model", John Vandermeer and Aaron King, Journal of Theoretical Biology 263 (2010) 237–241. Time-derivatives are as given in Eq 5 of the article. They were integrated via a second-order Runga-Kutta technique to obtain trajectories of the C vs. R point. The blue slope field is for dC/dR (=[dC/dt)/(dR/dt)]), and the zero-growth isoclines are per Equation 6 of the article.
Move the "Initial Condition" point and vary the parameters to understand the importance of isoclines and the nature of their points of intersection.
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