Nonlinear Difference Equations

András Simonovits
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András Simonovits: Hungarian Academy of Sciences

Chapter 3 in Mathematical Methods in Dynamic Economics, 2000, pp 68-88 from Palgrave Macmillan

Abstract: Abstract In this Chapter we shall outline those elements of the theory of timeinvariant nonlinear difference equations which will be used in the book. In Section 3.1 we shall investigate the existence and stability of fixed points, extending theorems for linear systems to nonlinear ones. In Section 3.2 we shall study limit cycles. In Section 3.3 the so-called chaotic dynamics will be analyzed where the paths depend sensitively on the initial states. Useful information can be found in Guckenheimer (1979), Guckenheimer and Holmes (1986),Grandmont (1986) and Devaney (1989).

Keywords: Lyapunov Function; Bifurcation Diagram; Global Stability; Logistic Equation; Schwarzian Derivative (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-0-230-51353-2_4

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DOI: 10.1057/9780230513532_4

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