Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps
There are few works about Neimark–Sacker bifurcating analysis on discrete dynamical systems with linear diffusion and delayed coupling under periodic/Neumann-boundary conditions. In this paper, we build up the framework for Neimark–Sacker bifurcations caused by Turing instability on high-dimensional...
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/716 |
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| author | Huanqin Hu Mingshu Peng Yingfei Qi |
| author_facet | Huanqin Hu Mingshu Peng Yingfei Qi |
| author_sort | Huanqin Hu |
| collection | DOAJ |
| description | There are few works about Neimark–Sacker bifurcating analysis on discrete dynamical systems with linear diffusion and delayed coupling under periodic/Neumann-boundary conditions. In this paper, we build up the framework for Neimark–Sacker bifurcations caused by Turing instability on high-dimensional discrete-time dynamical systems with symmetrical property in the linearized system. The fractional diffusion operator in higher-dimensional discrete dynamical systems is introduced and regular/chaotic Turing patterns are discovered by the computation of the largest Lyapunov exponents. |
| format | Article |
| id | doaj-art-6cc884e958964027981754326db0d9ff |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-6cc884e958964027981754326db0d9ff2025-08-20T02:53:38ZengMDPI AGFractal and Fractional2504-31102024-12-0181271610.3390/fractalfract8120716Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov MapsHuanqin Hu0Mingshu Peng1Yingfei Qi2College of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaCollege of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaCollege of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaThere are few works about Neimark–Sacker bifurcating analysis on discrete dynamical systems with linear diffusion and delayed coupling under periodic/Neumann-boundary conditions. In this paper, we build up the framework for Neimark–Sacker bifurcations caused by Turing instability on high-dimensional discrete-time dynamical systems with symmetrical property in the linearized system. The fractional diffusion operator in higher-dimensional discrete dynamical systems is introduced and regular/chaotic Turing patterns are discovered by the computation of the largest Lyapunov exponents.https://www.mdpi.com/2504-3110/8/12/716nonchaotic Rulkov modeldiscrete-time fractional diffusion operatorNeimark–Sacker bifurcationTuring patternsspatio–temporal chaos |
| spellingShingle | Huanqin Hu Mingshu Peng Yingfei Qi Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps Fractal and Fractional nonchaotic Rulkov model discrete-time fractional diffusion operator Neimark–Sacker bifurcation Turing patterns spatio–temporal chaos |
| title | Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps |
| title_full | Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps |
| title_fullStr | Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps |
| title_full_unstemmed | Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps |
| title_short | Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps |
| title_sort | rich dynamics caused by a fractional diffusion operator in nonchaotic rulkov maps |
| topic | nonchaotic Rulkov model discrete-time fractional diffusion operator Neimark–Sacker bifurcation Turing patterns spatio–temporal chaos |
| url | https://www.mdpi.com/2504-3110/8/12/716 |
| work_keys_str_mv | AT huanqinhu richdynamicscausedbyafractionaldiffusionoperatorinnonchaoticrulkovmaps AT mingshupeng richdynamicscausedbyafractionaldiffusionoperatorinnonchaoticrulkovmaps AT yingfeiqi richdynamicscausedbyafractionaldiffusionoperatorinnonchaoticrulkovmaps |