In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of Singer’s theorem, followed by the proof that it is generally not possible to provide closed formula for solutions.
An Example of Nonlinear Dynamical System: The Logistic Map
Giuseppe Orlando
;Giovanni Taglialatela
2021-01-01
Abstract
In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of Singer’s theorem, followed by the proof that it is generally not possible to provide closed formula for solutions.File in questo prodotto:
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