dx = x³ — y³, dy = 2xy² + 4x²y + 2y³. dt dt Construct a Lyapunov function of the form V(x, y) = ax²+ cy², where a and c are to be determined, to show that the single critical point of the system at the origin is unstable.
dx = x³ — y³, dy = 2xy² + 4x²y + 2y³. dt dt Construct a Lyapunov function of the form V(x, y) = ax²+ cy², where a and c are to be determined, to show that the single critical point of the system at the origin is unstable.
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
Section11.3: Euler's Method
Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.
Question
Consider the autonomous system: dx/dy= x^3-y^3 dy/dt = 2xy^2+4x^2y+2y^2. Construct a Lyapunov function of the form V (x, y) = ax2 + cy2
, where a and c are to be determined, to show that
the single critical point of the system at the origin is unstable.
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