Article
Computer Science, Interdisciplinary Applications
Miao Xue, Junting Gou, Yibo Xia, Qinsheng Bi
Summary: This paper investigates the normal form of a vector field with a codimension-3 zero-zero-Hopf bifurcation at the origin and develops a unified program to compute the coefficients of the normal form. By utilizing central manifold theory and normal form theory, expressions of all coefficients related to local bifurcations are provided. These expressions can be computed using a software program based on the symbolic language Maple.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics
Shangjiang Guo
Summary: This paper investigates the equivariant normal forms of semilinear functional differential equations in general Banach spaces. It is shown that the form of the reduced vector field depends not only on the information of the linearized system at the critical point but also on the inherent symmetry. The normal forms provide critical information about dynamical properties.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yehu Lv, Zhihua Liu
Summary: In this paper, a diffusive Brusselator model with gene expression time delay is proposed and its bifurcation behavior is studied. The conditions for Turing instability are derived, and the spatiotemporal dynamics in six different regions of the parameter plane are analyzed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Xinxin Qie, Quanbao Ji
Summary: This study investigated the stability and bifurcation of a nonlinear system model, finding that the system underwent two supercritical bifurcations and also observing saddle-node and torus bifurcations. Numerical simulations were carried out to validate the proposed approach.
Article
Mathematics, Applied
Yuting Ding, Gaoyang Liu, Liyuan Zheng
Summary: In this paper, the equivalence of the multiple time scales (MTS) method and the center manifold reduction (CMR) method for deriving the normal form of Hopf bifurcation for delayed reaction-diffusion equations is proven. The MTS method is generalized to delayed reaction-diffusion equations, providing a user-friendly approach for analyzing the stability of time-periodic solutions. Furthermore, the CMR method is outlined for the computation of normal form of Hopf bifurcation for delayed reaction-diffusion equations. It is shown that the two methods can derive equivalent up to the third order normal form of Hopf bifurcation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Chunyan Gao, Fangqi Chen
Summary: This study developed a general model of delayed p53 regulatory network in DNA damage response by introducing microRNA 192-mediated positive feedback loop. It was found that time delay can drive p53 oscillation and miR-192 affects the stability of system oscillations.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Interdisciplinary Applications
Minlong Li, Yibo Xia, Qinsheng Bi
Summary: This paper focuses on a vector field with codimension-3 triple Hopf bifurcation. The coefficients in the normal form and the nonlinear transformation are derived explicitly, and their relationships with the coefficients of the original vector field are established. A user friendly computer program is developed using these coefficients, and the universal unfolding of the normal form is obtained.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Youhua Qian, Danjin Zhang, Bingwen Lin
Summary: This study investigates the bursting oscillation mechanisms in systems with periodic excitation, analyzing different types of symmetric bursting oscillations and their bifurcation mechanisms through numerical simulations. The results show that these bursting oscillations exhibit symmetry in their patterns.
Article
Green & Sustainable Science & Technology
Banamali Maji, Samares Pal
Summary: The number of coral reefs is decreasing due to environmental and anthropogenic reasons, with Pterois volitans adding additional stress by decreasing herbivorous fish numbers. Algal overgrowth interferes with coral growth as they grow together on algal turfs. Parrotfish play a crucial role in coral enhancement by grazing, and this study analyzes the dynamics of the system with parrotfish and P. volitans as prey and predator respectively. The impact of prey refuge is considered, and stable coexistence regions for different parameter spaces are formulated and verified through numerical simulations.
ENVIRONMENT DEVELOPMENT AND SUSTAINABILITY
(2022)
Article
Mathematics, Interdisciplinary Applications
Rajinder Pal Kaur, Amit Sharma, Anuj Kumar Sharma
Summary: This paper analyzes the impact of fear effect and zooplankton refuge on a 3-D plankton-fish dynamical system. The findings suggest that these factors not only affect the dynamics of the ecosystem but may also terminate planktonic blooms.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Nan Deng, Luc R. Pastur, Laurette S. Tuckerman, Bernd R. Noack
Summary: Generically, a local bifurcation only affects a single solution branch. However, branches that are quite different may nonetheless share certain eigenvectors and eigenvalues, leading to coincident bifurcations.
Article
Engineering, Mechanical
Bence Szaksz, Gabor Stepan
Summary: This paper analyzes the interference of the elasticity and position control time delay of a single robotic arm from the perspective of nonlinear vibrations. The study shows that stabilizable and non-stabilizable parameter regions follow each other periodically, even for large spring stiffnesses and tiny time delays. Experimental data can serve as a guide for adjusting control gains.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics
Dongxu Geng, Hongbin Wang
Summary: This paper focuses on calculating the normal form on the center manifold up to the third order term at the double-Hopf singularity for general partial functional differential equations with nonlocal effects. Explicit formulas of the normal form are derived, providing an effective tool for establishing the existence of multi-periodic and quasi-periodic oscillations. Through the example of the Holling-Tanner predator-prey model with nonlocal competition, it is found that various spatio-temporal dynamics, including stable periodic and quasi-periodic solutions, can occur due to the nonlocal interaction.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Reed B. Cohen, Jiaxu Li
Summary: This paper analyzes the interactions between glucose, insulin, and glucagon in maintaining blood sugar levels through a dynamical system model. The study reveals the crucial roles of insulin and glucagon in balancing blood sugar levels.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ming Liu, Fanwei Meng, Dongpo Hu
Summary: This paper considers the stability and bifurcations of a genetic regulatory network, providing a complete stability analysis and characterizing the Hopf bifurcation and Bogdanov-Takens bifurcation analytically. Numerical examples and bifurcation curves are used to determine the stability of limit cycles and to illustrate other types of bifurcations. The results demonstrate rich bifurcation behavior in the genetic regulatory network.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Biology
Sara Hamis, James Yates, Mark A. J. Chaplain, Gibin G. Powathil
Summary: The study successfully simulated the treatment responses of LoVo cells to the anti-cancer drug AZD6738 by combining a systems pharmacology approach with an agent-based modelling approach, showing the potential of agent-based models in bridging the gap between in vitro and in vivo research in preclinical drug development.
BULLETIN OF MATHEMATICAL BIOLOGY
(2021)
Article
Biology
Linnea C. Franssen, Nikolaos Sfakianakis, Mark A. J. Chaplain
Summary: A three-dimensional hybrid atomistic-continuum model is developed to describe the invasive growth dynamics of individual cancer cells in tissue, accounting for phenotypic variation and transitions between epithelial-like and mesenchymal-like cell phenotypes. The model consists of partial and stochastic differential equations considering matrix-degrading enzyme concentrations and extracellular matrix density, calibrated to an in vitro invasion assay experiment of oral squamous cell carcinoma cells through parameter estimation and sensitivity analysis. This model provides a new theoretical basis for studying the invasion mechanisms of cancer cells.
JOURNAL OF THEORETICAL BIOLOGY
(2021)
Article
Multidisciplinary Sciences
Yunchen Xiao, Len Thomas, Mark A. J. Chaplain
Summary: Two different methods were proposed to estimate parameters within a partial differential equation model of cancer invasion, one based on approximate Bayesian computation and the other on a two-stage gradient matching method using a generalized additive model. Both methods performed well on simulated data, but the ability to estimate some model parameters deteriorated rapidly in the presence of simulated measurement error.
ROYAL SOCIETY OPEN SCIENCE
(2021)
Article
Oncology
Sara J. Hamis, Yury Kapelyukh, Aileen McLaren, Colin J. Henderson, C. Roland Wolf, Mark A. J. Chaplain
Summary: The study developed a mechanistic mathematical model to describe the synergistic action of dabrafenib and trametinib on ERK activity in BRAFV600E-mutant melanoma cells, elucidating the molecular mechanism underlying vertical inhibition of the BRAF-MEK-ERK cascade.
BRITISH JOURNAL OF CANCER
(2021)
Editorial Material
Biology
Philip K. Maini, Mark A. J. Chaplain, Mark A. Lewis, Jonathan A. Sherratt
BULLETIN OF MATHEMATICAL BIOLOGY
(2022)
Article
Mathematics
Esther S. Daus, Mariya Ptashnyk, Claudia Raithel
Summary: This article derives a fractional cross-diffusion system as the rigorous limit of a multispecies system of moderately interacting particles driven by Levy noise. The mutual interaction is motivated by the porous medium equation with fractional potential pressure. The approach is based on techniques developed by previous researchers, showing the convergence of a regularization of the empirical measure to the solution of a correspondingly regularized macroscopic system. Well-posedness and non-negativity of solutions are proved for the regularized macroscopic system, yielding the same results for the non-regularized fractional cross-diffusion system in the limit.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Biology
Chiara Villa, Alf Gerisch, Mark A. J. Chaplain
Summary: The formation of new vascular networks is crucial for tissue development and regeneration. Cluster-based vasculogenesis, a new mechanism involving the mobilization of cells from the bone marrow, plays a key role in connecting distant blood vessels in vivo. We propose a mathematical model to study the dynamics of cluster formation and investigate the effects of endogenous chemotaxis and matrix degradation through numerical and parametric analysis.
JOURNAL OF THEORETICAL BIOLOGY
(2022)
Article
Ecology
I. C. Engelhardt, D. Patko, Y. Liu, M. Mimault, G. de las Heras Martinez, T. S. George, M. MacDonald, M. Ptashnyk, T. Sukhodub, N. R. Stanley-Wall, N. Holden, T. J. Daniell, L. X. Dupuy
Summary: This study used live microscopy techniques to observe collective movement of B. subtilis bacteria in soil, resembling the behavior of bird flocks or fish schools. Genetic analysis suggests that this movement may be driven by diffusion of extracellular signaling molecules and influenced by physical obstacles and hydrodynamics in the soil environment.
Article
Agronomy
Andrew Mair, Lionel X. Dupuy, Mariya Ptashnyk
Summary: This study improves the existing model by incorporating root-oriented preferential flow, thereby enhancing the ability to describe and analyze water infiltration in vegetated soil.
Article
Mathematics, Applied
N. Bellomo, F. Brezzi, M. A. J. Chaplain
Summary: This editorial proposes modeling and simulation of mutating virus pandemics in a globally connected world. It is divided into three parts: a general framework that goes beyond deterministic population dynamics, the contents of the papers in this issue, and a critical analysis of research perspectives.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Biology
Dimitrios Katsaounis, Mark A. J. Chaplain, Nikolaos Sfakianakis
Summary: This paper addresses the question of identifying the migratory pattern and spread of individual cancer cells or small clusters of cancer cells when the macroscopic evolution of the cancer cell colony is determined by a specific partial differential equation (PDE). The authors demonstrate that the traditional understanding of the diffusion and advection terms of the PDE as responsible for random and biased motion of solitary cancer cells, respectively, is imprecise. Instead, they show that the drift term of the correct stochastic differential equation scheme should also take into account the divergence of the PDE diffusion. Numerical experiments and computational simulations are used to support their claims.
JOURNAL OF MATHEMATICAL BIOLOGY
(2023)
Article
Biochemical Research Methods
Matthias Mimault, Mariya Ptashnyk, Lionel X. Dupuy
Summary: This study successfully measured the mechanical properties of plant roots using a computational model, revealing the complex adaptability of roots to soil resistance. The results show that particle-based models can compute the growth of an entire organ at cellular resolution, which could significantly advance the studies of plant morphogenesis.
PLOS COMPUTATIONAL BIOLOGY
(2023)
Article
Agronomy
Andrew Mair, Lionel Dupuy, Mariya Ptashnyk
Summary: This study investigates how root-induced preferential flow redistributes soil water according to the architecture of a root system and how this may influence plant drought resistance. The findings suggest that an optimal preferential flow strength exists for minimizing water loss from the rooted zone and that this optimum differs with soil type. Additionally, a reduction in gravitropic response allows a root system to uptake more of the water that enters the soil.
FIELD CROPS RESEARCH
(2023)
Article
Mathematics, Applied
Chiara Villa, Mark A. Chaplain, Tommaso Lorenzi
Summary: This study investigates the emergence of phenotypic heterogeneity in vascularized tumors through mathematical modeling and numerical simulations. The results provide a theoretical basis for the empirical evidence that the phenotypic properties of cancer cells in vascularized tumors vary with the distance from the blood vessels, and establish a relation between the degree of tumor tissue vascularization and the level of intratumor phenotypic heterogeneity.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Mathematics
Chiara Villa, Mark A. J. Chaplain, Tommaso Lorenzi
Summary: This study investigates the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy using a mathematical model and numerical simulations. Findings suggest that tumour cell phenotypic properties vary with distance from blood vessels, hypoxic regions may support intra-tumour phenotypic heterogeneity, and hypoxia may favor the selection for chemoresistant phenotypic variants prior to treatment.
VIETNAM JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Kevin J. Painter, Thomas Hillen, Jonathan R. Potts
Summary: The use of nonlocal PDE models in describing biological aggregation and movement behavior has gained significant attention. These models capture the self-organizing and spatial sorting characteristics of cell populations and provide insights into how animals perceive and respond to their surroundings. By deriving and analyzing these models, we can better understand biological movement behavior and provide a basis for explaining sociological phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Nicola Bellomo, Massimo Egidi
Summary: This paper focuses on Herbert A. Simon's visionary theory of the Artificial World and proposes a mathematical theory to study the dynamics of organizational learning, highlighting the impact of decomposition and recombination of organizational structures on evolutionary changes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
Summary: This paper provides an overview of flows with moving boundaries and interfaces (MBI), which include fluid-particle and fluid-structure interactions, multi-fluid flows, and free-surface flows. These problems are frequently encountered in engineering analysis and design, and pose computational challenges that require core computational methods and special methods. The paper focuses on isogeometric analysis, complex geometries, incompressible-flow Space-Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian-Eulerian VMS (ALE-VMS) methods, and special methods developed in connection with these core methods.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)