PPT Slide
4 Numerical Analysis and Parameter Space
Definition 1: For one-dimensional mapping , there may be some special points that satisfy the equation . Such a point is called a fixed point of the mapping. Similarly, for n-dimensional mapping , there may be a special vector that satisfies the equation . Such a vector is called a fixed point of the n-dimensional mapping.
Definition 2: A flip (or period-doubling) bifurcation occurs when one of the eigenvalues of the Jacobian matrix of the mapping at the fixed point equals –1.
Stability: A fixed point of a n-dimensional mapping is stable if and only if its characteristic multipliers all lie within the unit circle in the complex plane.
characteristic multipliers: eigenvalues of the Jacobian matrix of the mapping at the fixed point