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Analysis of Stability, Bifurcation, and Chaos in Generalized Mackey-Glass Equations

2024/11/05 by Deepa Gupta, Sachin Bhalekar, Gupta, Deepa +1
Engineering · Mathematics · #26A33 #34K20 #Dynamical Systems (math.DS) #FOS: Mathematics #Material Science and Thermodynamics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2411.02865

openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such generalizations improve the model because the nonlocal operators viz. fractional derivatives are more suitable for the natural systems. We present the detailed stability and bifurcation analysis of the proposed models. We observe stable orbits, periodic oscillations, and chaos in these models. The parameter space is divided into a variety of regions, viz. stable region (delay independent), unstable region, single stable region, and stability/instability switch. Furthermore, we propose a control method for chaos in these general equations.

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