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Alfred Lotka (top) Vito Volterra

Predator-Prey Systems. Alfred Lotka (top) Vito Volterra. Interacting Populations. When two or more populations interact some very interesting (and complicated) behaviour ensues

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Alfred Lotka (top) Vito Volterra

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  1. Predator-Prey Systems Alfred Lotka (top) Vito Volterra

  2. Interacting Populations • When two or more populations interact some very interesting (and complicated) behaviour ensues • Predator-Prey models illustrate this and (in general) cannot be solved by simple methods – we will use an Euler Method approach • Some Key Term to learn: • Phase plane • Phase trajectories and portraits

  3. Rabbits and Wolves - From words to equations • The rabbit population is growing with a rate ‘k’ constant but is declining at a rate that is proportional to the rate constant ‘a’ at which the populations interact • The wolf population is declining (starvation) at a rate ‘r’ but is increasing at a rate that is proportional to the rate constant ‘b’ at which the populations interact

  4. Expressed as a system… Study section 9.6

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