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Mathematics, Interdisciplinary Applications
Haihua Zhou, Zejia Wang, Daming Yuan, Huijuan Song
Summary: This paper presents a mathematical model of tumor growth with angiogenesis and two time delays, studying the stability of stationary solutions and showing Hopf bifurcation under certain conditions. Numerical simulations explore the relationship among angiogenesis rate, time delays, and Hopf bifurcation.
CHAOS SOLITONS & FRACTALS
(2021)
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Mathematics
Wenhua He, Ruixiang Xing
Summary: In this paper, a free boundary problem modeling 3-dimensional multilayered tumor growth with time delay is considered. The introduction of time delay and spatial displacement poses challenges for bifurcation analysis due to the system's non-local nature. The novelty of this paper lies in exploring periodicity and symmetry to develop an effective method for bifurcation in this case.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
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Mathematics, Interdisciplinary Applications
Jingnan Wang, Hongbin Shi, Li Xu, Lu Zang
Summary: This paper discusses a model of tumor and lymphatic immune system interaction with two time delays, analyzing the stability of equilibrium and the existence of Hopf bifurcations. The numerical simulations show different behaviors under various time delays, providing insights into the biomedical significance of tumor and T lymphocyte dynamics.
CHAOS SOLITONS & FRACTALS
(2022)
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Economics
Mario Sportelli, Luigi De Cesare
Summary: This paper reconsiders the Goodwin 1967 growth-cycle model and combines the antagonistic relationship between wages and profits with the prey-predator conflict model. The authors propose an extension of Goodwin's basic model by adding two important elements of the business cycle theory, namely a finite time delay between investment orders and deliveries of finished capital goods, and a delayed reaction of real wages to the unemployment levels. The qualitative study of the system shows that without lags, the economic meaningful equilibrium is structurally stable; however, with positive time delays, the equilibrium loses its stability and periodic or non-periodic fluctuations may arise.
STRUCTURAL CHANGE AND ECONOMIC DYNAMICS
(2022)
Article
Mathematics
Xinyue Evelyn Zhao, Bei Hu
Summary: This paper investigates the bifurcation of a highly nonlinear and coupled PDE model describing the growth of arterial plaque in the early stage of atherosclerosis, establishing finite branches of symmetry-breaking stationary solutions. The results suggest that the asymmetric shapes of plaques in reality can be explained by the existence of non-radially symmetric solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Shihe Xu, Zuxing Xuan
Summary: This paper studies a free boundary problem for vascularized tumor growth with a necrotic core and time delays.Adequate conditions for the existence, uniqueness, and stability of the stationary solution to the problem are provided.The findings demonstrate that the time delay does not influence the final growth behavior of the tumor.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
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Mathematics, Applied
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Summary: Free boundary problems involve systems of partial differential equations with unknown domain boundaries. In this paper, a novel approach based on neural network discretization is developed for solving a modified Hele-Shaw problem, the existence of the numerical solution is theoretically established. The approach is further verified by computing symmetry-breaking solutions near the radially-symmetric branch, as well as non-radially symmetric solutions not characterized by any theorems.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Qinrui Dai, Mengjie Rong, Ren Zhang
Summary: In this paper, a delayed virotherapy model with infected and uninfected tumor cells and free virus is established. The stability and Hopf bifurcation of the model under different time delays are analyzed. The direction of Hopf bifurcation and stability of the bifurcated periodic solution are studied using center manifold theorem and normal form theory. The existence of Zero-Hopf bifurcation is proved. Numerical simulations show the results of theoretical calculations and demonstrate dynamic behaviors such as bistability, periodic coexistence, and chaotic behavior near Zero-Hopf and Bogdanov-Takens points of the system.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Haihua Zhou, Huijuan Song, Zejia Wang
Summary: This paper investigates a free boundary problem modeling tumor growth with angiogenesis and time delay in regulatory apoptosis. Two factors, apoptosis due to exceeding the natural lifespan and regulatory apoptosis with time delay, are introduced to cause tumor cell death. The existence, uniqueness, and asymptotic behavior of solutions are studied. The results show that the stabilities of stationary solutions are significantly affected by time delay in certain cases, leading to Hopf bifurcation at some threshold values. Numerical simulation results are presented to support the analytical findings, and the impact of angiogenesis on Hopf bifurcation is also discussed.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
Qingbin Gao, Xujie Zhang, Yifan Liu
Summary: In this study, we investigate the asymptotic stability of a linear love model with four independent time delays. By using a stability analysis framework, we accurately determine the stability switching boundaries where emotions change, and demonstrate the effectiveness of this framework through a case study.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Wenhua He, Ruixiang Xing, Bei Hu
Summary: This study investigates a free boundary problem modeling multilayer tumor growth with a small time delay. The research establishes the well-posedness of the problem and examines the stability of the stationary solution under non-flat perturbations. It also explores the effect of time delay on the size of the stationary tumor, providing interesting results with mathematical and biological implications.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
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Mathematics
Wenhua He, Ruixiang Xing
Summary: This paper discusses a model for tumor growth in the presence of drugs with high molecular mass, improving upon previous models by better accounting for nutrient and drug diffusion coefficients. Through parameter classification, the conditions for solutions and linear stability under non-radially symmetric perturbations were determined.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
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Mathematics, Applied
Shigui Ruan
Summary: This paper reviews recent research on the nonlinear dynamics of delayed differential equation models describing the interaction between tumor cells and effector cells of the immune system. The study investigates models with different numbers of delays and reveals various possible bifurcations and complex behaviors in the interaction dynamics. The results provide insights into the complexity of tumor-immune system interactions and pose interesting questions for future research.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
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Mathematical & Computational Biology
Sarita Bugalia, Jai Prakash Tripathi, Hao Wang
Summary: This paper proposes a delayed SEIR epidemic model with intervention strategies and recovery under resource constraints. It is found that time delays change the system dynamics through Hopf bifurcation and oscillations, and the intervention strength and treatment limitations have significant impacts on infection levels. The study highlights the importance of considering time delays in intervention and recovery in epidemic models.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2021)
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Computer Science, Artificial Intelligence
Changjin Xu, Zixin Liu, Maoxin Liao, Lingyun Yao
Summary: In this study, a novel fractional-order bank data model with two unequal time delays is established. The existence, non-negativeness and boundedness of the solution to the model are discussed, and the stability and the creation of Hopf bifurcation are investigated. Five new delay-independent stability conditions and bifurcation criteria are established, ensuring the stability behavior and the onset of Hopf bifurcation in the model. The role of time delay in stabilizing the system and controlling the generation of Hopf bifurcation is also explored. The study provides innovative conclusions and important theoretical guidance for maintaining the proper operation of banks.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
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Mathematical & Computational Biology
Shihe Xu, Meng Bai, Zhong Wang, Fangwei Zhang
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2018)
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Ecology
Meng Bai, Shihe Xu
JOURNAL OF BIOLOGICAL DYNAMICS
(2018)
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Mathematics
Shihe Xu, Fangwei Zhang
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2018)
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Mathematics, Interdisciplinary Applications
Shihe Xu, Fangwei Zhang
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Mathematics, Applied
Shihe Xu
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2020)
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Mathematics, Applied
Shihe Xu, Dan Su
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2020)
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Mathematics, Applied
Shihe Xu, Dan Su
BOUNDARY VALUE PROBLEMS
(2020)
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Mathematics, Interdisciplinary Applications
Shihe Xu, Meng Bai, Fangwei Zhang
Summary: This paper studies a mathematical model for solid vascular tumor growth with Gibbs-Thomson relation, discussing the impact of nutrients on tumor growth, as well as the results regarding existence, uniqueness, and nonexistence, and the discussion on the existence of symmetric and asymmetric solutions.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
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Mathematical & Computational Biology
Shihe Xu, Fangwei Zhang, Qinghua Zhou
Summary: This paper studies a mathematical model for solid avascular tumor growth with a time delay in regulatory apoptosis. The existence and uniqueness of a solution to the model are proved, and the long-time asymptotic behavior of the solutions is studied. The results show that the dynamical behavior of solutions to this model is similar to that of the corresponding quasi-stationary problem for some special parameter values.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2022)
Article
Mathematics, Applied
Shihe Xu, Zuxing Xuan
Summary: This paper studies a free boundary problem for vascularized tumor growth with a necrotic core and time delays.Adequate conditions for the existence, uniqueness, and stability of the stationary solution to the problem are provided.The findings demonstrate that the time delay does not influence the final growth behavior of the tumor.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Junde Wu, Shihe Xu
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2020)
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Mathematical & Computational Biology
Shihe Xu, Junde Wu
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2019)
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Computer Science, Information Systems
F. W. Zhang, W. W. Huang, J. Sun, Z. D. Liu, Y. H. Zhu, K. T. Li, S. H. Xu, Q. Li
Article
Mathematics, Applied
Shihe Xu, Meng Bai, Fangwei Zhang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2018)
Article
Mathematics
Shihe Xu
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
(2018)
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Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
