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lecture3b - Introduction to Computer Programming with...

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Introduction to Computer Programming with MATLAB CEE/MAE M20 Lecture 3b Predator-prey I CEE/MAE M20 What are we going to learn? Continuous versus discrete models Numerical integration: forward Euler method Flow control: for loop 2D plots 2 CEE/MAE M20 Outline 3 CEE/MAE M20 Outline I. Fundamentals of the predator-prey problem Background Mathematical model 3 CEE/MAE M20 Outline I. Fundamentals of the predator-prey problem Background Mathematical model II. Numerical Method 3 CEE/MAE M20 Outline I. Fundamentals of the predator-prey problem Background Mathematical model II. Numerical Method III. Example problem 3
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CEE/MAE M20 Outline I. Fundamentals of the predator-prey problem Background Mathematical model II. Numerical Method III. Example problem IV. Homework 3 4 CEE/MAE M20 http://www.leesonphoto.com/ Snowshoe hare and Canadian lynx 4 CEE/MAE M20 http://www.leesonphoto.com/ Snowshoe hare and Canadian lynx herbivore 4 CEE/MAE M20 http://www.leesonphoto.com/ Snowshoe hare and Canadian lynx herbivore carnivore 4 CEE/MAE M20 http://www.leesonphoto.com/ Snowshoe hare and Canadian lynx herbivore carnivore omnivore CEE/MAE M20 Observations 5
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CEE/MAE M20 Observations The populations of Canadian lynx and snowshoe hare observed from the pelt-trading records of the Hudson Bay Company over almost a century sciencesource2.pearsoncanada.ca 5 CEE/MAE M20 Observations The populations of Canadian lynx and snowshoe hare observed from the pelt-trading records of the Hudson Bay Company over almost a century Oscillating behavior of these two populations sciencesource2.pearsoncanada.ca 5 CEE/MAE M20 Observations The populations of Canadian lynx and snowshoe hare observed from the pelt-trading records of the Hudson Bay Company over almost a century Oscillating behavior of these two populations Predator peak lags slightly behind prey peak sciencesource2.pearsoncanada.ca 5 CEE/MAE M20 Mathematical Model Simplest mathematical model: Lotka–Volterra equations by Italian mathematician Vito Volterra and American mathematical biologist Alfred Lotka. Predator Prey 6 CEE/MAE M20 Mathematical Model Simplest mathematical model: Lotka–Volterra equations by Italian mathematician Vito Volterra and American mathematical biologist Alfred Lotka. Predator Prey α : growth rate of the prey 6 CEE/MAE M20 Mathematical Model Simplest mathematical model: Lotka–Volterra equations by Italian mathematician Vito Volterra and American mathematical biologist Alfred Lotka. Predator Prey γ : the death rate of the predator α : growth rate of the prey 6
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CEE/MAE M20 Mathematical Model Simplest mathematical model: Lotka–Volterra equations by Italian mathematician Vito Volterra and American mathematical biologist Alfred Lotka.
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