We studied the Lotka-Volterra model for predators and preys in class. There are systems of differential equations that model the growth and decline of populations of two competing species, they usually compete for their food supply. Let's see one! Let us work in a small region in of the Caribbean sea: Isla Paraiso. Let z be the population (in thousands) of the invasive lionfish that has become dominant in many places in the Caribbean, far from its natural Indo-Pacific waters. Let y be the population (in hundreds) of the local blacktip sharks. They both compete for the little fish around Isla Paraiso. The following system of differential equations models their populations: dr dt dy dt = x(2 - x - y) = y(3-2x - y) (a) What are the equilibrium solutions of the system? (b) What is the differential equation satisfied by y(r)? (c) Draw the phase portrait of this system.

We studied the Lotka-Volterra model for predators and preys in class. There are systems of differential equations that model the growth and decline of populations of two competing species, they usually compete for their food supply. Let's see one! Let us work in a small region in of the Caribbean sea: Isla Paraiso. Let z be the population (in thousands) of the invasive lionfish that has become dominant in many places in the Caribbean, far from its natural Indo-Pacific waters. Let y be the population (in hundreds) of the local blacktip sharks. They both compete for the little fish around Isla Paraiso. The following system of differential equations models their populations: dr dt dy dt = x(2 - x - y) = y(3-2x - y) (a) What are the equilibrium solutions of the system? (b) What is the differential equation satisfied by y(r)? (c) Draw the phase portrait of this system.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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