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Suppose that a certain pair of competing species are described by the system dx — x(4 — х — у) dt dy %3D у (2 + 2а — у — ах) dt where a > 0 is a parameter. а.) Find the critical points. Note that (2,2) is a critical point for all values of a. b.) Determine the nature of the critical point (2,2) for a = - and for a = : There 4 is a value of a between 0.75 and 1.25 where the nature of the critical point changes abruptly and it is called a bifurcation point, even though no critical points are gained or lost. Look for this value and denote this by ao.

Suppose that a certain pair of competing species are described by the system dx — x(4 — х — у) dt dy %3D у (2 + 2а — у — ах) dt where a > 0 is a parameter. а.) Find the critical points. Note that (2,2) is a critical point for all values of a. b.) Determine the nature of the critical point (2,2) for a = - and for a = : There 4 is a value of a between 0.75 and 1.25 where the nature of the critical point changes abruptly and it is called a bifurcation point, even though no critical points are gained or lost. Look for this value and denote this by ao.

Advanced Engineering Mathematics
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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Suppose that a certain pair of competing species are described by the system dx — x(4 — х — у) dt dy %3D у (2 + 2а — у — ах) dt where a > 0 is a parameter. а.) Find the critical points. Note that (2,2) is a critical point for all values of a. b.) Determine the nature of the critical point (2,2) for a = - and for a = : There 4 is a value of a between 0.75 and 1.25 where the nature of the critical point changes abruptly and it is called a bifurcation point, even though no critical points are gained or lost. Look for this value and denote this by ao.
Transcribed Image Text:Suppose that a certain pair of competing species are described by the system dx — x(4 — х — у) dt dy %3D у (2 + 2а — у — ах) dt where a > 0 is a parameter. а.) Find the critical points. Note that (2,2) is a critical point for all values of a. b.) Determine the nature of the critical point (2,2) for a = - and for a = : There 4 is a value of a between 0.75 and 1.25 where the nature of the critical point changes abruptly and it is called a bifurcation point, even though no critical points are gained or lost. Look for this value and denote this by ao.
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