000 ) ) Imagine the system of nonlinear ODE's below represents a population of hawks and crows, respectively: =1-y a.) Find the equilibrium points for this system. If necessary, round to two decimal places (e.g. 150.156 rounds to 150.16). b.) Use the Linearization Theorem to classify each equilibrium point. Show all necessary work, as we did throughout the lessons. Be sure to fully verify the validity of each classification by checking conditions of the theorem. c.) Are there any equilibrium points to which hawks and crows can converge, assuming the initial population sizes are not equal to any of the equilibrium points? Explain based on your understanding of your classifications.
000 ) ) Imagine the system of nonlinear ODE's below represents a population of hawks and crows, respectively: =1-y a.) Find the equilibrium points for this system. If necessary, round to two decimal places (e.g. 150.156 rounds to 150.16). b.) Use the Linearization Theorem to classify each equilibrium point. Show all necessary work, as we did throughout the lessons. Be sure to fully verify the validity of each classification by checking conditions of the theorem. c.) Are there any equilibrium points to which hawks and crows can converge, assuming the initial population sizes are not equal to any of the equilibrium points? Explain based on your understanding of your classifications.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:|cco
) Imagine the system of nonlinear ODE's below represents a population of hawks and crows,
respectively:
dt
1-y
= x² - y²
=
a.) Find the equilibrium points for this system. If necessary, round to two decimal places (e.g. 150.156
rounds to 150.16).
b.) Use the Linearization Theorem to classify each equilibrium point. Show all necessary work, as we
did throughout the lessons. Be sure to fully verify the validity of each classification by checking
conditions of the theorem.
c.) Are there any equilibrium points to which hawks and crows can converge, assuming the initial
population sizes are not equal to any of the equilibrium points? Explain based on your understanding
of your classifications.
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