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Consider the differential equation d = x(t) = ax(x² + y²) − xy³ dt d = y(t) = ay(x² + y²) + x²y² dt Transform this system to polar co-ordinates. Then, determine the values for a such that the origin is stable but not asymptotically stable asymptotically stable ⚫ unstable.

Consider the differential equation d = x(t) = ax(x² + y²) − xy³ dt d = y(t) = ay(x² + y²) + x²y² dt Transform this system to polar co-ordinates. Then, determine the values for a such that the origin is stable but not asymptotically stable asymptotically stable ⚫ unstable.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Consider the differential equation d = x(t) = ax(x² + y²) − xy³ dt d = y(t) = ay(x² + y²) + x²y² dt Transform this system to polar co-ordinates. Then, determine the values for a such that the origin is stable but not asymptotically stable asymptotically stable ⚫ unstable.
Transcribed Image Text:Consider the differential equation d = x(t) = ax(x² + y²) − xy³ dt d = y(t) = ay(x² + y²) + x²y² dt Transform this system to polar co-ordinates. Then, determine the values for a such that the origin is stable but not asymptotically stable asymptotically stable ⚫ unstable.
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