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Control and synchronization of Julia sets of discrete fractional Ising models

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  • Lu, Xiaoling
  • Sun, Weihua

Abstract

The discrete fractional complex dynamic system generated by the renormalization transformation corresponding to Ising model on a two-dimensional equilateral triangular lattice is introduced in this paper. Then the Julia set of the fractional system is defined, and the controller based on a coordinate transformation is designed to control the Julia set. In addition, two nonlinear coupling controllers are constructed to achieve the synchronization of Julia sets of two discrete fractional systems with different parameters and different orders. The simulation diagrams are given to verify the efficacy of controllers.

Suggested Citation

  • Lu, Xiaoling & Sun, Weihua, 2024. "Control and synchronization of Julia sets of discrete fractional Ising models," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000924
    DOI: 10.1016/j.chaos.2024.114541
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    References listed on IDEAS

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