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Boundary analysis and energy feedback control of fractional-order extended Malkus–Robbins dynamo system

Author

Listed:
  • Hou, Yi-You
  • Lin, Ming-Hung
  • Saberi-Nik, Hassan
  • Arya, Yogendra

Abstract

In this paper, the fractional-order extended Malkus-Robbins dynamo system (FOEMRD) is introduced. Additionally, the stability, complexity diagrams, Lyapunov dimension, Lyapunov exponents, and bifurcation diagrams of the system are studied. Also, we estimate the global Mittag-Leffler positive invariant sets and global Mittag-Leffler attractive sets of the proposed system. In addition, the Hamilton energy function of the FOEMRD system is computed by the Helmholtz theorem. Next, we design an energy feedback controller to control the chaos. Due to the relationship of Hamilton energy with the occurrence of chaos, the energy control method is very efficient and powerful. The applicability of the presented theories was proven with numerical simulations and related diagrams.

Suggested Citation

  • Hou, Yi-You & Lin, Ming-Hung & Saberi-Nik, Hassan & Arya, Yogendra, 2024. "Boundary analysis and energy feedback control of fractional-order extended Malkus–Robbins dynamo system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004740
    DOI: 10.1016/j.chaos.2024.114922
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