Approximate formulas and algorithms for constructing central manifolds of dynamic systems

New approaches to obtain approximations of the second and higher orders for the central manifolds of non-hyperbolic equilibria of continuous- and discrete-time dynamic systems are proposed. The formulas derived below lead to new practical algorithms for constructing central manifolds. The formulas and algorithms are general in the sense that they can be used to construct central manifolds in terms of the original equations and are applicable to the cases in which the linearization matrix has an arbitrary order of degeneracy.