Stability of fixed points in generalized fractional maps of the orders $$0&lt; \alpha &lt;1$$

Edelman, Mark

doi:10.1007/s11071-023-08359-0

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The Unstable Orbits Of the Fractional Difference Logistic Map1

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2023

2024

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Cited by 7 publications

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“…In this section, we only address fixed points relevant to the construction of the impulse control scheme. A more detailed discussion on types of fixed points in fractional order systems can be found in [37][38][39].…”

Section: The Unstable Orbits Of the Fractional Difference Logistic Mapmentioning

confidence: 99%

Finite-Time Stabilization of Unstable Orbits in the Fractional Difference Logistic Map

Uzdila,

Telksniene,

Telksnys

et al. 2023

Fractal Fract

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A control scheme for finite-time stabilization of unstable orbits of the fractional difference logistic map is proposed in this paper. The presented technique is based on isolated perturbation impulses used to correct the evolution of the map’s trajectory after it deviates too far from the neighborhood of the unstable orbit, and does not require any feedback control loops. The magnitude of the control impulses is determined by means of H-rank algorithm, which helps to reveal the pseudo-manifold of non-asymptotic convergence of the fractional difference logistic map. Numerical experiments are used to illustrate the effectiveness and the feasibility of the proposed approach, which is applicable beyond the studied fractional difference logistic map.

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Section: The Unstable Orbits Of the Fractional Difference Logistic Mapmentioning

confidence: 99%