Assume that V (x,y) is a global Lyapunov function about the origin for the differential equation d x = f₁(x, y) dt d y = f2(x, y). dt Prove that the origin is the only equilibrium point for the ODE.
Assume that V (x,y) is a global Lyapunov function about the origin for the differential equation d x = f₁(x, y) dt d y = f2(x, y). dt Prove that the origin is the only equilibrium point for the ODE.
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 1YT
Question
Transcribed Image Text:Assume that V (x,y) is a global Lyapunov function about the origin for the differential
equation
d
x = f₁(x, y)
dt
d
y = f2(x, y).
dt
Prove that the origin is the only equilibrium point for the ODE.
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,