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Li-Yorke chaos in a class of controlled delay difference equations

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  • Liang, Wei
  • Lv, Xiaolin

Abstract

A class of controlled delay difference equations is considered. Proof of the existence of chaos in the sense of Li-Yorke in the controlled system is given by applying the snap-back repeller theorem. Conditions for the existence of chaos are weak and lots of functions can be taken as controllers, which facilitates the chaotification of delay difference equations. One illustrative example is provided with computer simulations.

Suggested Citation

  • Liang, Wei & Lv, Xiaolin, 2022. "Li-Yorke chaos in a class of controlled delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001527
    DOI: 10.1016/j.chaos.2022.111942
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    References listed on IDEAS

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    1. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    2. Zongcheng Li, 2014. "Anticontrol of Chaos for a Class of Delay Difference Equations Based on Heteroclinic Cycles Connecting Repellers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
    3. Khellat, Farhad & Ghaderi, Akashe & Vasegh, Nastaran, 2011. "Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 934-939.
    4. Masoller, Cristina & Zanette, nindexDamianDamia’an H., 2001. "Anticipated synchronization in coupled chaotic maps with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 359-366.
    5. Zongcheng Li & Shutang Liu & Wei Li & Qingli Zhao, 2015. "Chaotification for a Class of Delay Difference Equations Based on Snap-Back Repellers," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, October.
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    Cited by:

    1. Zhang, Yongjun & Liang, Wei & Lv, Xiaolin, 2023. "Existence of chaos in controlled first-order partial difference equations with general delay controllers," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Zhi Liu & Rongwei Guo, 2023. "Stabilization of the GLV System with Asymptotically Unbounded External Disturbances," Mathematics, MDPI, vol. 11(21), pages 1-12, October.
    3. Liang, Wei & Zhang, Yongjun & Zhang, Xuanxuan, 2024. "Chaotic behavior of two discrete-time coupled neurons with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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