Difference between revisions of "Predator prey"

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Revision as of 15:57, 21 October 2012

This page contains a description predator prey model that is used as a running example throughout the text. A detailed description of the dynamics of this system is presented in Chapter 3 - Examples and these dynamics are analyzed in Chapter 4 - Dynamic Behavior. A state space feedback controller is designed in Chapter 6 - State Feedback. This page brings together this material into a single place, to illustrate the application of analysis and design tools for this system. Links to MATLAB scripts are included that generate the analysis and figures described here.

System Description

The predator-prey problem refers to an ecological system in which we have two species, one of which feeds on the other. This type of system has been studied for decades and is known to exhibit interesting dynamics. The figure below shows a historical record taken over 90 years for a population of lynxes versus a population of hares (MacLulich, 1937).

  Predprey-photo.png   Predprey-graph.png  

Figure 2.6: Predator versus prey. The photograph on the left shows a Canadian lynx and a snowshoe hare, the lynx’s primary prey. The graph on the right shows the populations of hares and lynxes between 1845 and 1935 in a section of the Canadian Rockies (MacLuluch, 1937). The data were collected on an annual basis over a period of 90 years. (Photograph copyright Tom and Pat Leeson.)

Discrete Time Model

Continuous Time Model