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索引
4 Numerical Analysis and Parameter Space
4.1 Fundamental Theories
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