Chaos and bifurcation analysis of tumor-immune controlled system with time delay
This paper establishes a delayed discrete tumor-immune model with feedback controller. The results indicate that the controlled system exhibits a trend from chaotic state to stability. The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifol...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-04-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016825001097 |
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| author | Danni Wang Hongli Yang Liangui Yang |
| author_facet | Danni Wang Hongli Yang Liangui Yang |
| author_sort | Danni Wang |
| collection | DOAJ |
| description | This paper establishes a delayed discrete tumor-immune model with feedback controller. The results indicate that the controlled system exhibits a trend from chaotic state to stability. The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifold theorem, and bifurcation theory. The Gram–Schmidt orthonormalization (GSO) method is used to interpret the attractor properties of uncontrolled and controlled systems, it is revealed that the attractors of controlled systems are smaller than those of uncontrolled systems, and the theoretical and numerical results are consistent. In addition, this research indicates that noise can cause significant changes in the amplitude of time-delay free system oscillations, with little impact on the period. Interestingly, the dynamic characteristics of noise in time-delay systems are not significantly affected by noise. |
| format | Article |
| id | doaj-art-6742d0595b9742ed94744328734fee00 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-6742d0595b9742ed94744328734fee002025-02-07T04:47:14ZengElsevierAlexandria Engineering Journal1110-01682025-04-01119267284Chaos and bifurcation analysis of tumor-immune controlled system with time delayDanni Wang0Hongli Yang1Liangui Yang2School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaCorresponding author.; School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaThis paper establishes a delayed discrete tumor-immune model with feedback controller. The results indicate that the controlled system exhibits a trend from chaotic state to stability. The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifold theorem, and bifurcation theory. The Gram–Schmidt orthonormalization (GSO) method is used to interpret the attractor properties of uncontrolled and controlled systems, it is revealed that the attractors of controlled systems are smaller than those of uncontrolled systems, and the theoretical and numerical results are consistent. In addition, this research indicates that noise can cause significant changes in the amplitude of time-delay free system oscillations, with little impact on the period. Interestingly, the dynamic characteristics of noise in time-delay systems are not significantly affected by noise.http://www.sciencedirect.com/science/article/pii/S1110016825001097Chaos controlStabilityBifurcationTime delayNoise |
| spellingShingle | Danni Wang Hongli Yang Liangui Yang Chaos and bifurcation analysis of tumor-immune controlled system with time delay Alexandria Engineering Journal Chaos control Stability Bifurcation Time delay Noise |
| title | Chaos and bifurcation analysis of tumor-immune controlled system with time delay |
| title_full | Chaos and bifurcation analysis of tumor-immune controlled system with time delay |
| title_fullStr | Chaos and bifurcation analysis of tumor-immune controlled system with time delay |
| title_full_unstemmed | Chaos and bifurcation analysis of tumor-immune controlled system with time delay |
| title_short | Chaos and bifurcation analysis of tumor-immune controlled system with time delay |
| title_sort | chaos and bifurcation analysis of tumor immune controlled system with time delay |
| topic | Chaos control Stability Bifurcation Time delay Noise |
| url | http://www.sciencedirect.com/science/article/pii/S1110016825001097 |
| work_keys_str_mv | AT danniwang chaosandbifurcationanalysisoftumorimmunecontrolledsystemwithtimedelay AT hongliyang chaosandbifurcationanalysisoftumorimmunecontrolledsystemwithtimedelay AT lianguiyang chaosandbifurcationanalysisoftumorimmunecontrolledsystemwithtimedelay |