Explanation Recall: Our task is to consider a system consisting of two species-one a predator and one a prey-and to devise a pair of differential equations that describes their interactions and whose solutions gives their populations. To be specific, let the predator be foxes, whose population at time t ≥ 0 is F ( t ) , and let the prey be hares, whose population at time t ≥ 0 is H ( t ) . Here are the assumptions that underlie the model. (1) When the hare population (prey) is sparse, the fox population decreases exponentially, while encounters between hares and foxes increase the fox population (the hares are the food supply). (2) When the fox population (predators) is sparse, the hare population increases exponentially, while encounters between hares and foxes deplete the hare population (the foxes eat the hares). Verification: Trace 3 solution curve in FH -plane as shown below in Figure1.

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

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ISBN: 9780134996103

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 9.5, Problem 3QC

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To explain: The reason for a closed solution curve in FH-plane that represents a fox and hare population oscillates in a cyclic way.

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Chapter 9.5, Problem 2QC

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Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - The solution to the initial value problem y(t) = 2...

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The reason for a closed solution curve in FH -plane that represents a fox and hare population oscillates in a cyclic way.

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To explain: The reason for a closed solution curve in FH-plane that represents a fox and hare population oscillates in a cyclic way.

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