Method for determining Hopf bifurcation points of a periodic state description of a technical system; computer program and computer program product executing the method; storage medium, computer memory, electric carrier signal, and data carrier storing the computer program; and method for downloading a computer program containing the method

A method for determining Hopf bifurcation points of a periodic state description of a technical system having oscillations and satisfying an equation:

• f(x′(t),x(t),λ)=0,
• which comprises the following steps:
• a) determining a value for a parameter λ and calculating a stationary solution (x,λ) by solving
• F(x,λ)=0,
• b) calculating Jacobi matrices C, G,
• c) setting up a function
• {tilde over (g)}(z)=cT(G+zC)−1 b,
• b, c being orthonormalized random vectors,
• d) separating a constant term g∞
• {tilde over (g)}(z)=∞+g(z),
• e) calculating a number of turns per unit length WZ of a function g, evaluated along an imaginary axis:
• 8 WZ = W ⁡ ( g ⁡ ( ik ) ;
• 0 , ∞ ) = ( N 1 - N r + P r - P 1 ) ⁢ π 2 ,
• f) determining a monotonicity behavior of a real part R(g(ik)) of a function g(ik),
• g) determining if a Hopf bifurcation point has been found by using the numbers of turns per unit length WZ of the function g(ik), and by using the monotonicity behavior of the real part R(g(ik)) of the function g(ik):
• if the Hopf bifurcation point has been found, determining an approximation for a frequency of an oscillation and, if appropriate, carrying out an inverse iteration for accurately determining an actual frequency,
• if the Hopf bifurcation point has not been found, checking if λ≦λmax, and
• h) repeating steps a) to f) if the Hopf bifurcation point has not been found and if λ≦λmax.