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# In 14–24, you will need a computer and a | Ch 5.3 - 19E

ISBN: 9780321747730 43

## Solution for problem 19E Chapter 5.3

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition

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Problem 19E

In 14–24, you will need a computer and a programmed version of the vectorized classical fourth-order Runge–Kutta algorithm. (At the instructor’s discretion, other algorithms may be used.)Predator–Prey Model. The Volterra–Lotka predator– prey model predicts some rather interesting behavior that is evident in certain biological systems. For example, suppose you fix the initial population of prey but increase the initial population of predators. Then the population cycle for the prey becomes more severe in the sense that there is a long period of time with a reduced population of prey followed by a short period when the population of prey is very large. To demonstrate this behavior, use the vectorized Runge–Kutta algorithm for systems with h = 0.5 to approximate the populations of prey x and of predators y over the period [0,5] that satisfy the Volterra–Lotka system under each of the following initial conditions:(a) (b) (c)

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Warring States Period (Zhanguo) 479-221 BCE The Historical and Socio-Political context of Early China Western Zhou Rulership • The Western Zhou (1045 – 771 BCE) polity consisted of numerous clan-based regions between the Yellow and Yangtze rivers th th • After defeating the Shang Dynasty (14 – 11 centuries BCE) the Western Zhou kings appointed...

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