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H4. Consider an ODE d dx(t) = fi(x,y) ty(t) = f(x,y), d dt that has precisely two equilibrium points, both of which are saddle points, at (0,0) and (1,0). Once again, sketch the phase portrait where there is a nullcline that connects (0,0) with (1,0). Classify this null-cline and give necessary conditions on f1(x, 0), f1(0,0), ƒ2(0,0), ƒ2(x,0), f₁(1,0) and f₂(1,0). Hint: Write down your thought process, even if you don't manage to solve this problem.

H4. Consider an ODE d dx(t) = fi(x,y) ty(t) = f(x,y), d dt that has precisely two equilibrium points, both of which are saddle points, at (0,0) and (1,0). Once again, sketch the phase portrait where there is a nullcline that connects (0,0) with (1,0). Classify this null-cline and give necessary conditions on f1(x, 0), f1(0,0), ƒ2(0,0), ƒ2(x,0), f₁(1,0) and f₂(1,0). Hint: Write down your thought process, even if you don't manage to solve this problem.

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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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H4. Consider an ODE d dx(t) = f(x,y) d ty(t) = ƒ2(x,y), that has precisely two equilibrium points, both of which are saddle points, at (0,0) and (1,0). Once again, sketch the phase portrait where there is a nullcline that connects (0,0) with (1,0). Classify this null-cline and give necessary conditions on f1(x, 0), f1(0,0), ƒ2(0,0), ƒ2(x,0), f₁(1,0) and f₂(1,0). Hint: Write down your thought process, even if you don't manage to solve this problem.
Transcribed Image Text:H4. Consider an ODE d dx(t) = f(x,y) d ty(t) = ƒ2(x,y), that has precisely two equilibrium points, both of which are saddle points, at (0,0) and (1,0). Once again, sketch the phase portrait where there is a nullcline that connects (0,0) with (1,0). Classify this null-cline and give necessary conditions on f1(x, 0), f1(0,0), ƒ2(0,0), ƒ2(x,0), f₁(1,0) and f₂(1,0). Hint: Write down your thought process, even if you don't manage to solve this problem.
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