Unformatted text preview: T the threshold for the di±erential equation. Whenever the initial position y is less than this threshold the solution y ( t ) → 0. Figure 1. Slope ²ield for y ° = − r y (1 − y/T )-0.5 0.5 1 1.5 2 2.5 3 3.5 4-1-0.5 0.5 1 1.5 2 We conclude the lecture to relating everything we’ve done so far with population dynamics. Say that we have a population of size P = P ( t ) at time t . We keep track of two properties: • There is an environmental carrying capacity K . That is, if P > K then the population will decrease in size because the population has exceeded its resources. 1...
View Full Document
- Spring '09
- Population Dynamics, Order theory, Monotonic function, Convex function