Mathematical Biology: II: Spatial Models and Biomedical Applications

Cited by (1,000)

Items 101–200 of 1,000

1. The neural origins of shell structure and pattern in aquatic mollusks
   Alistair Nicol Boettiger, Bard Ermentrout, GEORGE F. OSTER · 2009 · Proceedings of the National Academy of Sciences
2. Consumer Fronts, Global Change, and Runaway Collapse in Ecosystems
   Brian Reed Silliman, Michael W. McCoy, Christine Angelini, Robert Douglas Holt, John N. Griffin, Johan van de Koppel · 2013 · Annual Review of Ecology Evolution and Systematics
3. The Economics of Non-Convex Ecosystems: Introduction
   Partha Sarathi Dasgupta, Karl-Göran Mäler · 2006 · Kluwer Academic Publishers eBooks
4. Pattern formation, spatial externalities and regulation in coupled economic–ecological systems
   William Brock, Anastasios Xepapadeas · 2009 · Journal of Environmental Economics and Management
5. Cooperative pattern formation in multi-component bacterial systems through reciprocal motility regulation
   Agnese I. Curatolo, Nan Zhou, Yongfeng Zhao, Chenli Liu, Adrian Daerr, Julien Tailleur, J. Huang · 2020 · Nature Physics
6. An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence
   K. Böttger, Haralampos Hatzikirou, Anja Voß-Böhme, Elisabetta Ada Cavalcanti‐Adam, Miguel A. Herrero, Andreas Deutsch · 2015 · PLoS Computational Biology
7. Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative
   Kolade Matthew Owolabi · 2018 · The European Physical Journal Plus
8. The ideal free distribution as an evolutionarily stable strategy
   Robert Stephen Cantrell, Chris Cosner, Donald Lee Deangelis, Vı́ctor Padrón · 2007 · Journal of Biological Dynamics
9. Pattern formation in a spatialS–Imodel with non-linear incidence rates
   Gui‐Quan Sun, Zhen Jin, Quan‐Xing Liu, Li Li · 2007 · Journal of Statistical Mechanics Theory and Experiment
10. Synthetic mammalian pattern formation driven by differential diffusivity of Nodal and Lefty
    Ryoji Sekine, Tatsuo Shibata, Miki Ebisuya · 2018 · Nature Communications
11. Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations
    Anotida Madzvamuse, Hussaini S. Ndakwo, Raquel Barreira · 2014 · Journal of Mathematical Biology
12. Mathematics in Sociology
    Christofer Edling · 2002 · Annual Review of Sociology
13. A Delay Reaction-Diffusion Model of the Spread of Bacteriophage Infection
    Stephen A. Gourley, Yang Kuang · 2004 · SIAM Journal on Applied Mathematics
14. Fisher Waves in the Strong Noise Limit
    Oskar Hallatschek, Kirill S. Korolev · 2009 · Physical Review Letters
15. Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control
    William Brock, Anastasios Xepapadeas · 2007 · Journal of Economic Dynamics and Control
16. A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18 F-FMISO-PET
    Russell C. Rockne, Andrew Daniel Trister, Joshua Jacobs, Andrea J. Hawkins-Daarud, Maxwell Lewis Neal, Kristi R. G. Hendrickson, Maciej M. Mrugała, Jason K. Rockhill, Paul E. Kinahan, Kenneth A. Krohn et al. · 2014 · Journal of The Royal Society Interface
17. Effects of Fear and Additional Food in a Delayed Predator–Prey Model
    Sudeshna Mondal, Alakes Maiti, G. P. Samanta · 2018 · Biophysical Reviews and Letters
18. Small Regulatory RNAs May Sharpen Spatial Expression Patterns
    Erel Levine, Peter T. McHale, Herbert Levine · 2007 · PLoS Computational Biology
19. Key Features of Turing Systems are Determined Purely by Network Topology
    Xavier Diego, Luciano Marcon, Patrick Müller, James Sharpe · 2018 · Physical Review X
20. Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
    Hao Wang A, Yurij Salmaniw · 2023 · Journal of Mathematical Biology
21. The marbled crayfish: a new model organism for research on development, epigenetics and evolutionary biology
    Günter Vogt · 2008 · Journal of Zoology
22. The two-regime method for optimizing stochastic reaction–diffusion simulations
    Mark B. Flegg, Stephen Jonathan Chapman, Radek Erban A · 2011 · Journal of The Royal Society Interface
23. ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES
    Nicola Bellomo, Abdelghani Bellouquid, Juanjo Nieto, Juan Soler · 2011 · Mathematical Models and Methods in Applied Sciences
24. How Active Mechanics and Regulatory Biochemistry Combine to Form Patterns in Development
    Peter A. Gross, K. Vijay Kumar, Stephan W. Grill · 2017 · Annual Review of Biophysics
25. Understanding the Dynamics of Sustainable Social-Ecological Systems: Human Behavior, Institutions, and Regulatory Feedback Networks
    John Martin Anderies · 2014 · Bulletin of Mathematical Biology
26. Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability
    Wei-Rong Zhong, Yuanzhi Shao, Zhenhui He · 2006 · Physical Review E
27. Critical behavior of the susceptible-infected-recovered model on a square lattice
    Tânia Tomé, Robert M. Ziff · 2010 · Physical Review E
28. Tensorial Minkowski functionals and anisotropy measures for planar patterns
    Gerd E. Schröder‐Turk, Sebastian C. Kapfer, B. Breidenbach, Claus Beisbart, Klaus R Mecke · 2009 · Journal of Microscopy
29. Pattern Formation in a Model for Mountain Pine Beetle Dispersal: Linking Model Predictions to Data
    S. Strohm, Rebecca C. Tyson, James A. Powell · 2013 · Bulletin of Mathematical Biology
30. A Nonlinear Stability Analysis of Vegetative Turing Pattern Formation for an Interaction–Diffusion Plant-Surface Water Model System in an Arid Flat Environment
    Bonni J. Kealy-Dichone, David J. Wollkind · 2011 · Bulletin of Mathematical Biology
31. Two-stage Turing model for generating pigment patterns on the leopard and the jaguar
    Ren-Han Liu, Sy-Sang Liaw, Philip K. Maini · 2006 · Physical Review E
32. Front acceleration by dynamic selection in Fisher population waves
    Olivier Bénichou, Vincent Calvez, Nicolas Meunier, Raphaël Voituriez · 2012 · Physical Review E
33. Traveling waves in a nonlocal dispersal Kermack-McKendrickepidemic model
    Fei-Ying Yang, Yan Li, Wan‐Tong Li, Zhi‐Cheng Wang · 2013 · Discrete and Continuous Dynamical Systems - B
34. SEXUAL SELECTION AND THE EVOLUTION OF COSTLY FEMALE PREFERENCES: SPATIAL EFFECTS
    Troy Day · 2000 · Evolution
35. Computational models for mechanics of morphogenesis
    Matthew A. Wyczalkowski, Zi Chen, Benjamen A. Filas, Victor D. Varner, Larry A. Taber · 2012 · Birth Defects Research Part C Embryo Today Reviews
36. ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS
    Boris Andreïanov, Mostafa Bendahmane, Ricardo Ruíz-Baier · 2010 · Mathematical Models and Methods in Applied Sciences
37. Traveling Wave Solutions for a Class of Predator–Prey Systems
    Wenzhang Huang · 2012 · Journal of Dynamics and Differential Equations
38. Bounded-noise-induced transitions in a tumor-immune system interplay
    Alberto d’Onofrio · 2010 · Physical Review E
39. Fractional Reaction-Diffusion Equations
    R. K. Saxena, Arak M. Mathai, Hans Joachim Haubold · 2006 · Astrophysics and Space Science
40. Spiral Waves in Nonlocal Equations
    Carlo R. Laing · 2005 · SIAM Journal on Applied Dynamical Systems
41. Fluctuations uncover a distinct class of traveling waves
    Gabriel Bîrzu, Oskar Hallatschek, Kirill S. Korolev · 2018 · Proceedings of the National Academy of Sciences
42. Range expansion promotes cooperation in an experimental microbial metapopulation
    Manoshi Sen Datta, Kirill S. Korolev, Ivana Cvijović, Carmel Dudley, Jeff Gore · 2013 · Proceedings of the National Academy of Sciences
43. Partial differential equations for self-organization in cellular and developmental biology
    Ruth E. Baker, Eamonn A. Gaffney, Philip K. Maini · 2008 · Nonlinearity
44. Spatial patterns of a predator-prey model with cross diffusion
    Gui‐Quan Sun, Zhen Jin, Li Li, Mainul Haque, Bai-Lian Li · 2012 · Nonlinear Dynamics
45. Application of Discontinuous Galerkin Methods for Reaction-Diffusion Systems in Developmental Biology
    Jianfeng Zhu, Yong‐Tao Zhang, Stuart A. Newman, Mark Alber · 2008 · Journal of Scientific Computing
46. Convergence in competition models with small diffusion coefficients
    Vivian Hutson, Y. Lou, Konstantin Mischaikow · 2004 · Journal of Differential Equations
47. In order to make spatial statistics computationally feasible, we need to forget about the covariance function
    Daniel Simpson, Finn Lindgren, Håvard Rue · 2011 · Environmetrics
48. Facing Low Regularity in Chemotaxis Systems
    Johannes Lankeit, Michael Winkler · 2019 · Jahresbericht der Deutschen Mathematiker-Vereinigung
49. Stencils with isotropic discretization error for differential operators
    Michael Patra, Mikko Karttunen · 2005 · Numerical Methods for Partial Differential Equations
50. Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study
    Alex Viguerie, Alessandro Veneziani, Guillermo Lorenzo, Davide Baroli, Nicole Aretz, Alessia Patton, Thomas E. Yankeelov, Alessandro Reali, Thomas J. R. Hughes, Ferdinando Auricchio · 2020 · Computational Mechanics
51. Mode-locking via dissipative Faraday instability
    Nikita Tarasov, Auro M. Perego, Dmitry V. Churkin, Kęstutis Staliūnas, Sergei K. Turitsyn · 2016 · Nature Communications
52. Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback
    Denis Menshykau, Odyssé Michos, Christine Lang, Lisa Conrad, Andrew P. McMahon, Dagmar Iber · 2019 · Nature Communications
53. Spatiotemporal dynamics of a diffusive consumer‐resource model with explicit spatial memory
    Yongli Song, Junping Shi, Hao Wang A · 2021 · Studies in Applied Mathematics
54. Topology Optimization of the Stator for Minimizing Cogging Torque of IPM Motors
    Jae Seok Choi, Kazuhiro Izui, Shinji Nishiwaki, Atsushi Kawamoto, Tsuyoshi Nomura · 2011 · IEEE Transactions on Magnetics
55. Existence of spatial patterns in a predator–prey model with self- and cross-diffusion
    Lakshmi Narayan Guin · 2013 · Applied Mathematics and Computation
56. A two-grid method for mixed finite-element solution of reaction-diffusion equations
    Li Wu, Myron B. Allen · 1999 · Numerical Methods for Partial Differential Equations
57. Force Localization in Contracting Cell Layers
    Carina M. Dunlop, Ulrich S. Schwarz · 2011 · Physical Review Letters
58. Kinetic equations for reaction-subdiffusion systems: Derivation and stability analysis
    A. Yadav, Werner Horsthemke · 2006 · Physical Review E
59. Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay
    Weihua Jiang, Hongbin Wang, Xun Cao · 2018 · Journal of Dynamics and Differential Equations
60. Mathematical models for cell migration: a non-local perspective
    Li Chen, Kevin J. Painter, Christina Surulescu, Anna Zhigun · 2020 · Philosophical Transactions of the Royal Society B Biological Sciences
61. Pathogens can Slow Down or Reverse Invasion Fronts of their Hosts
    Frank M. Hilker, Mark A. Lewis, Hiromi Seno, Michel R. Langlais, Horst Malchow · 2005 · Biological Invasions
62. A Moving Grid Finite Element Method for the Simulation of Pattern Generation by Turing Models on Growing Domains
    Anotida Madzvamuse, Philip K. Maini, Andy Wathen · 2005 · Journal of Scientific Computing
63. The role of residence times in two-patch dengue transmission dynamics and optimal strategies
    Sunmi ‍Lee, Carlos Castillo‐Chávez · 2015 · Journal of Theoretical Biology
64. Digit patterning during limb development as a result of the BMP-receptor interaction
    Amarendra Badugu, Conradin Kraemer, Philipp Germann, Denis Menshykau, Dagmar Iber · 2012 · Scientific Reports
65. Three-dimensional Simulation of Fracture Repair in the Human Tibia
    Damien Jerome Lacroix, P.J. Prendergast · 2002 · Computer Methods in Biomechanics & Biomedical Engineering
66. On the mechanochemical theory of biological pattern formation with application to vasculogenesis
    J. D. Murray · 2003 · Comptes Rendus Biologies
67. The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation
    Václav Klika, Ruth E. Baker, Denis J. Headon, Eamonn A. Gaffney · 2011 · Bulletin of Mathematical Biology
68. EMPIRICAL MODE DECOMPOSITION: APPLICATIONS ON SIGNAL AND IMAGE PROCESSING
    Jean‐Claude Nunes, Éric Deléchelle · 2008 · Advances in Adaptive Data Analysis
69. Population biology and rarity: on the complexity of density dependence in insect—plant interactions
    William E. Kunin · 1997 · Springer eBooks
70. Invasion entire solutions in a competitionsystem with nonlocal dispersal
    Wan‐Tong Li, Li Zhang, Guo‐Bao Zhang · 2014 · Discrete and Continuous Dynamical Systems
71. Mechanical interactions in bacterial colonies and the surfing probability of beneficial mutations
    Fred Farrell, Matti Gralka, Oskar Hallatschek, Bartłomiej Waclaw · 2017 · Journal of The Royal Society Interface
72. Theory of Turing Patterns on Time Varying Networks
    Julien Petit, Ben Lauwens, Duccio Fanelli, Timotéo Carletti · 2017 · Physical Review Letters
73. The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
    Hans G. Othmer, Kevin J. Painter, David M. Umulis, C. Xue · 2009 · Mathematical Modelling of Natural Phenomena
74. The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
    Jonathan Dawes · 2010 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
75. Wave Patterns Driven by Chemomechanical Instabilities in Responsive Gels
    Vincent Labrot, P. De Kepper, J. Boissonade, István Szalai, Fabienne Gauffre · 2005 · The Journal of Physical Chemistry B
76. Higher-order convergence analysis for interior and boundary layers in a semi-linear reaction-diffusion system networked by a $ k $-star graph with non-smooth source terms
    Dilip Sarkar, Shridhar Kumar, Pratibhamoy Das, Higinio Ramos · 2024 · Networks and Heterogeneous Media
77. Radiotherapy planning for glioblastoma based on a tumor growth model: improving target volume delineation
    Jan Unkelbach, Bjoern H. Menze, Ender Konukoğlu, Florian Dittmann, Matthieu Le, Nicholas Ayache, Helen A Shih · 2014 · Physics in Medicine and Biology
78. Engineering in Medicine To Address the Challenge of Cancer Drug Resistance: From Micro- and Nanotechnologies to Computational and Mathematical Modeling
    Morgan Craig, Adrianne L. Jenner, Bumseok Namgung, Luke P. Lee, Aaron J. Goldman · 2020 · Chemical Reviews
79. Externally Controllable Molecular Communication
    Tadashi Nakano, Shouhei Kobayashi, Tatsuya Suda, Yutaka Okaie, Yasushi Hiraoka, Tokuko Haraguchi · 2014 · IEEE Journal on Selected Areas in Communications
80. CROSS-DIFFUSION-DRIVEN PATTERN FORMATION AND SELECTION IN A MODIFIED LESLIE–GOWER PREDATOR–PREY MODEL WITH FEAR EFFECT
    Renji Han, Lakshmi Narayan Guin, Binxiang Dai · 2020 · Journal of Biological Systems
81. Predator–prey systems in streams and rivers
    Frank M. Hilker, Mark A. Lewis · 2009 · Theoretical Ecology
82. TUMOR-IMMUNE SYSTEM INTERACTION: MODELING THE TUMOR-STIMULATED PROLIFERATION OF EFFECTORS AND IMMUNOTHERAPY
    Alberto d’Onofrio · 2006 · Mathematical Models and Methods in Applied Sciences
83. Numerical simulations of multicomponent ecological models with adaptive methods
    Kolade Matthew Owolabi, Kailash C. Patidar · 2016 · Theoretical Biology and Medical Modelling
84. Extracellular matrix environment influences chondrogenic pattern formation in limb bud micromass culture: Experimental verification of theoretical models
    Takashi Miura, Kohei Shiota · 2000 · The Anatomical Record
85. Collective behavior of brain tumor cells: The role of hypoxia
    Evgeniy Khain, Mark Katakowski, Scott Hopkins, Alexandra Szalad, Xuguang Zheng, Feng Jiang, Michael Chopp · 2011 · Physical Review E
86. Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies
    Mohammad Kohandel, Mehran Kardar A, Michael Milosevic, Siv Sivaloganathan · 2007 · Physics in Medicine and Biology
87. Axonal Velocity Distributions in Neural Field Equations
    Ingo Bojak, David T. J. Liley · 2010 · PLoS Computational Biology
88. Fundamental properties of cooperative contagion processes
    Li Chen, Fakhteh Ghanbarnejad, Dirk Brockmann · 2017 · New Journal of Physics
89. Pattern formation in chemically interacting active rotors with self-propulsion
    Benno Liebchen, Michael E. Cates, Davide Marenduzzo · 2016 · Soft Matter
90. Spatial Memory and Taxis-Driven Pattern Formation in Model Ecosystems
    Jonathan R. Potts, Mark A. Lewis · 2019 · Bulletin of Mathematical Biology
91. Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
    Abdul Majeed, Mohsin Kamran, Muhammad Kashif Iqbal, Dumitru Bǎleanu · 2020 · Advances in Difference Equations
92. The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy
    Benjamin Ribba, Tomás Alarcón, Karen Marron, Philip K. Maini, Zvia Agur · 2004 · Lecture notes in computer science
93. Stability and Traveling Fronts in Lotka-Volterra Competition Models with Stage Structure
    J. F. M. Al-Omari, Stephen A. Gourley · 2003 · SIAM Journal on Applied Mathematics
94. Systems biology of robustness and homeostatic mechanisms
    H. Frederik Nijhout, Janet A. Best, Michael C. Reed · 2018 · WIREs Systems Biology and Medicine
95. Biological Control Through Intraguild Predation: Case Studies in Pest Control, Invasive Species and Range Expansion
    Caroline Bampfylde, Mark A. Lewis · 2007 · Bulletin of Mathematical Biology
96. Stochastic reaction and diffusion on growing domains: Understanding the breakdown of robust pattern formation
    Thomas E. Woolley, Ruth E. Baker, Eamonn A. Gaffney, Philip K. Maini · 2011 · Physical Review E
97. DETERMINISTIC AND STOCHASTIC ANALYSIS OF A NONLINEAR PREY-PREDATOR SYSTEM
    Malay Bandyopadhyay, C. G. Chakrabarti · 2003 · Journal of Biological Systems
98. EVOLUTION OF ANTIBIOTIC RESISTANCE BY HUMAN AND BACTERIAL NICHE CONSTRUCTION
    Maciej F. Boni, Marcus William Feldman · 2005 · Evolution
99. The Resolution of Inflammation: A Mathematical Model of Neutrophil and Macrophage Interactions
    Joanne L. Dunster, Helen Mary Byrne, John R. King · 2014 · Bulletin of Mathematical Biology
100. Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems
     Anotida Madzvamuse, Andy H. W. Chung, Chandrasekhar Venkataraman · 2015 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences