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....

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Main Authors: Wenxin Zhang, Lijun Pei
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:Electronic Research Archive
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Online Access:https://www.aimspress.com/article/doi/10.3934/era.2025057
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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.
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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