Bifurcation and chaos in N-type and S-type muscular blood vessel models
In this paper, we have constructed two muscular blood vessel systems influenced by external disturbances by using the non-autonomous delayed differential equation (DDE). As an important physiological structure of the human body, muscle blood vessels participate in many activities such as blood flow....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2025057 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850151303606435840 |
|---|---|
| author | Wenxin Zhang Lijun Pei |
| author_facet | Wenxin Zhang Lijun Pei |
| author_sort | Wenxin Zhang |
| collection | DOAJ |
| description | In this paper, we have constructed two muscular blood vessel systems influenced by external disturbances by using the non-autonomous delayed differential equation (DDE). As an important physiological structure of the human body, muscle blood vessels participate in many activities such as blood flow. Many diseases are associated with abnormal dynamics of muscle blood vessels. From a mathematical point of view, vasospasm is caused by a chaotic state of blood vessels. Vasospasm is the manifestation of this disease in the vascular system, which can cause blood vessel blockage and even harm human health when it is serious. We conducted the dynamical analysis of the S-type and N-type muscular blood vessel systems by utilizing bifurcation diagrams, time histories, and pseudo-phase portraits, and investigated the effects of different parameters on these systems. Specifically, when parameters change, rich dynamical phenomena occur, such as equilibria, periodic solutions, quasi-periodic solutions, Hopf bifurcation, and chaos, as well as the route of period-doubling bifurcation to chaos. Meanwhile, we analyzed approximate analytical solutions by using the method of multiple scales (MMS) and determined the stability of steady-state solutions through the Routh-Hurwitz criterion. The results indicate that the MMS can deduce better analytical results for some non-autonomous DDEs. |
| format | Article |
| id | doaj-art-58fb1bfefddb414184c8af2f6c899084 |
| institution | OA Journals |
| issn | 2688-1594 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-58fb1bfefddb414184c8af2f6c8990842025-08-20T02:26:19ZengAIMS PressElectronic Research Archive2688-15942025-03-013331285130510.3934/era.2025057Bifurcation and chaos in N-type and S-type muscular blood vessel modelsWenxin Zhang0Lijun Pei1School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, ChinaIn this paper, we have constructed two muscular blood vessel systems influenced by external disturbances by using the non-autonomous delayed differential equation (DDE). As an important physiological structure of the human body, muscle blood vessels participate in many activities such as blood flow. Many diseases are associated with abnormal dynamics of muscle blood vessels. From a mathematical point of view, vasospasm is caused by a chaotic state of blood vessels. Vasospasm is the manifestation of this disease in the vascular system, which can cause blood vessel blockage and even harm human health when it is serious. We conducted the dynamical analysis of the S-type and N-type muscular blood vessel systems by utilizing bifurcation diagrams, time histories, and pseudo-phase portraits, and investigated the effects of different parameters on these systems. Specifically, when parameters change, rich dynamical phenomena occur, such as equilibria, periodic solutions, quasi-periodic solutions, Hopf bifurcation, and chaos, as well as the route of period-doubling bifurcation to chaos. Meanwhile, we analyzed approximate analytical solutions by using the method of multiple scales (MMS) and determined the stability of steady-state solutions through the Routh-Hurwitz criterion. The results indicate that the MMS can deduce better analytical results for some non-autonomous DDEs.https://www.aimspress.com/article/doi/10.3934/era.2025057muscular blood vessel systemschaosmmsnon-autonomous ddehopf bifurcation |
| spellingShingle | Wenxin Zhang Lijun Pei Bifurcation and chaos in N-type and S-type muscular blood vessel models Electronic Research Archive muscular blood vessel systems chaos mms non-autonomous dde hopf bifurcation |
| title | Bifurcation and chaos in N-type and S-type muscular blood vessel models |
| title_full | Bifurcation and chaos in N-type and S-type muscular blood vessel models |
| title_fullStr | Bifurcation and chaos in N-type and S-type muscular blood vessel models |
| title_full_unstemmed | Bifurcation and chaos in N-type and S-type muscular blood vessel models |
| title_short | Bifurcation and chaos in N-type and S-type muscular blood vessel models |
| title_sort | bifurcation and chaos in n type and s type muscular blood vessel models |
| topic | muscular blood vessel systems chaos mms non-autonomous dde hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2025057 |
| work_keys_str_mv | AT wenxinzhang bifurcationandchaosinntypeandstypemuscularbloodvesselmodels AT lijunpei bifurcationandchaosinntypeandstypemuscularbloodvesselmodels |