Local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors

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Author(s)

  • Qing-Rui Yang
  • Xian-Feng Li
  • Zhe Yang
  • Andrew Y.-T. Leung

Detail(s)

Original languageEnglish
Article number2450168
Journal / PublicationInternational Journal of Modern Physics C
Volume36
Issue number1
Online published21 Jun 2024
Publication statusPublished - Jan 2025

Abstract

The paper devotes to the synthesis of local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors. The discrete model gives rise to a two-dimensional non-invertible map, whose basins of attraction have complicated topological structures due to the intrinsic multi-stability. The influences of joint parameters on the local dynamics are presented in great details. Both theoretical and numerical results are plotted on the two-dimensional parametric planes. To show more detailed bifurcation structure, the isoclines are extended to higher periodic orbits for detecting the cusps of resonant entrainments. Invariant manifolds and critical curves are employed to illustrate the global dynamics of the model vividly. The tangency and intersections of invariant manifolds expound the process of erosions of basins of attraction. The global bifurcations of basins of attraction are deduced dynamically by critical curves.

Research Area(s)

  • Local and global dynamics, bifurcations, basins of attraction, invariant manifolds, critical curves

Bibliographic Note

Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

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