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Fractional-order singular logistic map: Stability, bifurcation and chaos analysis

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  • Nosrati, Komeil
  • Shafiee, Masoud

Abstract

Recently fractional calculus started to gain much importance due to its applications to the mathematical modeling of real phenomena with memory effect. Besides, singular modeling, which has been accompanied by exhibiting more complicated dynamics rather than standard models, can reveal the instability mechanism of wide-range of physical systems. Utilizing these two applicable techniques of modeling, a generalization of the logistic growth model, which takes into account the effects of memory and economic interest, is suggested in this paper. Besides mathematical analysis and extracting new results on the equilibrium points and local stability studies of discrete-time commensurate fractional-order singular (FOS) state space systems, some basic dynamical properties and qualitative analysis of the new chaotic FOS logistic map are studied, either numerically or analytically, to explore the impacts of real order and economic interest on the presented system in biological contexts.

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  • Nosrati, Komeil & Shafiee, Masoud, 2018. "Fractional-order singular logistic map: Stability, bifurcation and chaos analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 224-238.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:224-238
    DOI: 10.1016/j.chaos.2018.08.023
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    References listed on IDEAS

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    2. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    3. Area, I. & Nieto, J.J., 2021. "Power series solution of the fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    4. Huang, Lilian & Liu, Jin & Xiang, Jianhong & Zhang, Zefeng & Du, Xiuli, 2022. "A construction method of N-dimensional non-degenerate discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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    7. Zhang, Xuefeng & Zhao, Zeli, 2020. "Robust stabilization for rectangular descriptor fractional order interval systems with order 0 < α < 1," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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