Global nonlinear polynomial models: Structure, term clusters and fixed points

In this paper, it is shown that the number and location of the fixed points of global nonlinear polynomials can be specified in terms of the term clusters and cluster coefficients of the respective models. It is also shown that if the structure (that is, the model basis) of a nonlinear polynomial model of degree l includes all possible terms then such a model will always have l nontrivial fixed points. In modeling problems, where the estimated polynomials are to reproduce fundamental invariants of the original system, this situation will not always be welcome and therefore suggests that the structure of polynomial models should be carefully chosen. Ways of achieving this are briefly mentioned.