Solving nonlinear recursions

S. Rabinovich, G. Berkolaiko, S. Havlin

Research output: Contribution to journalArticlepeer-review

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A general method to map a polynomial recursion on a matrix linear one is suggested. The solution of the recursion is represented as a product of a matrix multiplied by the vector of initial values. This matrix is product of transfer matrices whose elements depend only on the polynomial and not on the initial conditions. The method is valid for systems of polynomial recursions and for polynomial recursions of arbitrary order. The only restriction on these recurrent relations is that the highest-order term can be written in explicit form as a function of the lower-order terms (existence of a normal form). A continuous analog of this method is described as well.

Original languageEnglish
Pages (from-to)5828-5836
Number of pages9
JournalJournal of Mathematical Physics
Issue number11
StatePublished - Nov 1996


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