Consider the differential equation d dx(t) = ax+y+x³ d =x-y, First, sketch the nullclines of the differential equation, determine any equilibria, and linearise the system near these equilibria as a function of the parameter a. Then, determine the local stability of the origin as a function of the model parameter a.
Consider the differential equation d dx(t) = ax+y+x³ d =x-y, First, sketch the nullclines of the differential equation, determine any equilibria, and linearise the system near these equilibria as a function of the parameter a. Then, determine the local stability of the origin as a function of the model parameter a.
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
Question
Transcribed Image Text:Consider the differential equation
d
dx(t) = ax+y+x³
d
=x-y,
First, sketch the nullclines of the differential equation, determine any equilibria, and
linearise the system near these equilibria as a function of the parameter a.
Then, determine the local stability of the origin as a function of the model parameter a.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,