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

Qing-Rui Yang, Xian-Feng Li, Zhe Yang and Andrew Y.-T. Leung
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Qing-Rui Yang: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, P. R. China
Xian-Feng Li: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, P. R. China
Zhe Yang: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, P. R. China
Andrew Y.-T. Leung: ��Saint Francis University, 2 Chui Ling Ln, Tseung Kwan O, Hong Kong‡City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 01, 1-14

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.

Keywords: Local and global dynamics; bifurcations; basins of attraction; invariant manifolds; critical curves (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501687

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