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Math Help - Equilibrium Points in the Lorentz System

  1. #1
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    Equilibrium Points in the Lorentz System

    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
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  2. #2
    Junior Member
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    Re: Equilibrium Points in the Lorentz System

    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.
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