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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Qing-Rui Yang & Xian-Feng Li & Zhe Yang & Andrew Y.-T. Leung, 2025. "Local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-14, January.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:01:n:s0129183124501687
    DOI: 10.1142/S0129183124501687
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