Analysis of Stability, Bifurcation, and Chaos in Generalized Mackey-Glass Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912105715728384 |
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| author | Gupta, Deepa Bhalekar, Sachin |
| author_facet | Gupta, Deepa Bhalekar, Sachin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of Stability, Bifurcation, and Chaos in Generalized Mackey-Glass Equations Gupta, Deepa Bhalekar, Sachin Dynamical Systems 26A33, 34K20 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. |
| title | Analysis of Stability, Bifurcation, and Chaos in Generalized Mackey-Glass Equations |
| topic | Dynamical Systems 26A33, 34K20 |
| url | https://arxiv.org/abs/2411.02865 |