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Resonant bifurcation of feed-forward chains and application in image contrast enhancement

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  • Wang, Wenlong
  • Lin, Xiao
  • Zhang, Chunrui

Abstract

This paper discusses the 1:1 resonant Hopf bifurcations and nilpotent singularity of non-semisimple for feed-forward chains with delay. The analytical formulas show that at synchrony-breaking bifurcation points the center manifold inherits a feed-forward structure. Using this structure, an analytical formula of normal form is derived to provide that near the points of 1:1 resonant Hopf bifurcation the amplitude of periodic solutions grows at the surprising rate of μ16 due to resonance, rather than the expected rate of μ12. This phenomenon provides an enhancement algorithm for low contrast images.

Suggested Citation

  • Wang, Wenlong & Lin, Xiao & Zhang, Chunrui, 2021. "Resonant bifurcation of feed-forward chains and application in image contrast enhancement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 294-307.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:294-307
    DOI: 10.1016/j.matcom.2021.03.004
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    References listed on IDEAS

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    1. Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    2. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    3. Zhang, Chunrui & Zhang, Xianhong & Zhang, Yazhou, 2018. "Dynamic properties of feed-forward neural networks and application in contrast enhancement for image," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 281-290.
    4. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
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