Hello, i cannot solve this problem:
The Lorentz System is
dX/dt = s(Y-X)
dY/dt = r*X-Y-Z*X
dZ/dt = X*Y-b*Z
Find for all values r >1 and positive values of s and b all equilibrium points, and explain what happens when r -> 1+.
Thanks alot
Hello, i cannot solve this problem:
The Lorentz System is
dX/dt = s(Y-X)
dY/dt = r*X-Y-Z*X
dZ/dt = X*Y-b*Z
Find for all values r >1 and positive values of s and b all equilibrium points, and explain what happens when r -> 1+.
Thanks alot
Solution: The Lorentz system is
dx/dt=s(y-x)
dy/dt=r*x-y-z*x
dz/dt=x*y-b*z
let s,r and b are positive
assume s=10
r=28
b=8/3
if r>1 then two additional critical point appear
(±vb(r-1),±vb(r-1),r-1)
=(±v8/2(28-1),±v8/2(28-1),28-1)
=(±8.48,±8.48,27)
this pair of equilibrium points are stable only if r<s(s+b+3/s-b-1)
if r<1 then there is only one equilibrium point which is at the origin,this point corresponds to no conversion.