Dynamical Analysis Of Fractional Order Generalized Logistic Map
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912022188261376 |
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| author | Bhalekar, Sachin Chevala, Janardhan Gade, Prashant M. |
| author_facet | Bhalekar, Sachin Chevala, Janardhan Gade, Prashant M. |
| contents | In this work, we propose a generalization to the classical logistic map. The generalized map preserves most properties of the classical map and has richer dynamics as it contains the fractional order and one more parameter. We propose the stability bounds for each equilibrium point. The detailed bifurcation analysis with respect to both parameters is presented using the bifurcation diagrams in one and two dimensions. The chaos in this system is controlled using delayed feedback. We provide some non-linear feedback controllers to synchronize the system. The multistability in the proposed system is also discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_07174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Analysis Of Fractional Order Generalized Logistic Map Bhalekar, Sachin Chevala, Janardhan Gade, Prashant M. Dynamical Systems 26A33, 39A28, 39A30, 39A33 In this work, we propose a generalization to the classical logistic map. The generalized map preserves most properties of the classical map and has richer dynamics as it contains the fractional order and one more parameter. We propose the stability bounds for each equilibrium point. The detailed bifurcation analysis with respect to both parameters is presented using the bifurcation diagrams in one and two dimensions. The chaos in this system is controlled using delayed feedback. We provide some non-linear feedback controllers to synchronize the system. The multistability in the proposed system is also discussed. |
| title | Dynamical Analysis Of Fractional Order Generalized Logistic Map |
| topic | Dynamical Systems 26A33, 39A28, 39A30, 39A33 |
| url | https://arxiv.org/abs/2409.07174 |