## Nelson, Patrick W.

Compute Distance To:
 Author ID: nelson.patrick-w Published as: Nelson, Patrick W.; Nelson, P. W.; Nelson, Patrick more...less External Links: MGP
 Documents Indexed: 22 Publications since 1992, including 1 Book Co-Authors: 20 Co-Authors with 18 Joint Publications 447 Co-Co-Authors
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### Co-Authors

 1 single-authored 6 Perelson, Alan S. 6 Ulsoy, A. Galip 6 Yi, Sun 3 Bortz, David M. 2 Ciupe, Stanca M. 1 Bivort, B. L. 1 Ciupe, M. S. 1 Coombs, Daniel 1 Criminale, William O. jun. 1 Dat Duc Bui 1 Duan, Shiming 1 Forde, Jonathan E. 1 Gilchrist, Michael A. 1 Hyman, James M. 1 Jackson, Thomas Luther 1 Murray, James Dickson 1 Omenn, Gilbert S. 1 Pietropaolo, Massimo 1 Radcliffe, Andrew John 1 Ribeiro, Ruy M. 1 Seth, Daniel L. 1 Smith, Noah A. 1 Zou, Weiping
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### Serials

 3 Mathematical Biosciences 3 Mathematical Biosciences and Engineering 2 Bulletin of Mathematical Biology 1 Discrete Mathematics 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 IEEE Transactions on Automatic Control 1 Studies in Applied Mathematics 1 Mathematical and Computer Modelling 1 SIAM Review 1 Journal of Vibration and Control 1 Journal of Theoretical Biology
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### Fields

 11 Biology and other natural sciences (92-XX) 7 Ordinary differential equations (34-XX) 6 Systems theory; control (93-XX) 4 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

21 Publications have been cited 1,185 times in 809 Documents Cited by Year
Mathematical analysis of HIV-1 dynamics in vivo. Zbl 1078.92502
Perelson, Alan S.; Nelson, Patrick W.
1999
Mathematical analysis of delay differential equation models of HIV-1 infection. Zbl 0992.92035
Nelson, Patrick W.; Perelson, Alan S.
2002
A model of HIV-1 pathogenesis that includes an intracellular delay. Zbl 0942.92017
Nelson, Patrick W.; Murray, James D.; Perelson, Alan S.
2000
Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. Zbl 1086.92022
Ciupe, M. S.; Bivort, B. L.; Bortz, D. M.; Nelson, P. W.
2006
An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Zbl 1060.92038
Nelson, Patrick W.; Gilchrist, Michael A.; Coombs, Daniel; Hyman, James M.; Perelson, Alan S.
2004
Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Zbl 1334.92225
Bortz, D. M.; Nelson, P. W.
2004
Controllability and observability of systems of linear delay differential equations via the matrix Lambert $$W$$ function. Zbl 1367.93084
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2008
Eigenvalue assignment via the Lambert W function for control of time-delay systems. Zbl 1269.93036
Yi, S.; Nelson, P. W.; Ulsoy, A. G.
2010
Applications of Sturm sequences to bifurcation analysis of delay differential equation models. Zbl 1257.34050
Forde, Jonathan; Nelson, Patrick
2004
Design of observer-based feedback control for time-delay systems with application to automotive powertrain control. Zbl 1298.93173
Yi, Sun; Ulsoy, A. Galip; Nelson, Patrick W.
2010
Traveling-wave solutions of the diffusively corrected kinematic-wave model. Zbl 0994.90031
Nelson, P.
2002
Modeling the mechanisms of acute hepatitis B virus infection. Zbl 1455.92022
Ciupe, Stanca M.; Ribeiro, Ruy M.; Nelson, Patrick W.; Perelson, Alan S.
2007
Model selection and mixed-effects modeling of HIV infection dynamics. Zbl 1296.92123
Bortz, D. M.; Nelson, P. W.
2006
Delay differential equations via the matrix Lambert $$W$$ function and bifurcation analysis: application to machine tool chatter. Zbl 1131.34056
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2007
Time-delay systems. Analysis and control using the Lambert W function. Zbl 1209.93002
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2010
Modeling viral infections. Zbl 1025.92010
Perelson, Alan S.; Nelson, Patrick W.
2002
Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing. Zbl 0766.35074
Dat Duc Bui; Nelson, P.
1992
Modeling dynamic changes in type 1 diabetes progression: quantifying $$\beta$$-cell variation after the appearance of islet-specific autoimmune responses. Zbl 1190.53052
Nelson, Patrick; Smith, Noah; Ciupe, Stanca; Zou, Weiping; Omenn, Gilbert S.; Pietropaolo, Massimo
2009
Semi-regular graphs of minimum independence number. Zbl 1030.05059
2004
Limit cycle-strange attractor competition. Zbl 1141.34323
Criminale, W. O.; Jackson, T. L.; Nelson, P. W.
2004
Analysis and control of time delay systems using the LambertWDDE Toolbox. Zbl 1275.93034
Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A. Galip
2014
Analysis and control of time delay systems using the LambertWDDE Toolbox. Zbl 1275.93034
Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A. Galip
2014
Eigenvalue assignment via the Lambert W function for control of time-delay systems. Zbl 1269.93036
Yi, S.; Nelson, P. W.; Ulsoy, A. G.
2010
Design of observer-based feedback control for time-delay systems with application to automotive powertrain control. Zbl 1298.93173
Yi, Sun; Ulsoy, A. Galip; Nelson, Patrick W.
2010
Time-delay systems. Analysis and control using the Lambert W function. Zbl 1209.93002
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2010
Modeling dynamic changes in type 1 diabetes progression: quantifying $$\beta$$-cell variation after the appearance of islet-specific autoimmune responses. Zbl 1190.53052
Nelson, Patrick; Smith, Noah; Ciupe, Stanca; Zou, Weiping; Omenn, Gilbert S.; Pietropaolo, Massimo
2009
Controllability and observability of systems of linear delay differential equations via the matrix Lambert $$W$$ function. Zbl 1367.93084
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2008
Modeling the mechanisms of acute hepatitis B virus infection. Zbl 1455.92022
Ciupe, Stanca M.; Ribeiro, Ruy M.; Nelson, Patrick W.; Perelson, Alan S.
2007
Delay differential equations via the matrix Lambert $$W$$ function and bifurcation analysis: application to machine tool chatter. Zbl 1131.34056
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip
2007
Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. Zbl 1086.92022
Ciupe, M. S.; Bivort, B. L.; Bortz, D. M.; Nelson, P. W.
2006
Model selection and mixed-effects modeling of HIV infection dynamics. Zbl 1296.92123
Bortz, D. M.; Nelson, P. W.
2006
An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Zbl 1060.92038
Nelson, Patrick W.; Gilchrist, Michael A.; Coombs, Daniel; Hyman, James M.; Perelson, Alan S.
2004
Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Zbl 1334.92225
Bortz, D. M.; Nelson, P. W.
2004
Applications of Sturm sequences to bifurcation analysis of delay differential equation models. Zbl 1257.34050
Forde, Jonathan; Nelson, Patrick
2004
Semi-regular graphs of minimum independence number. Zbl 1030.05059
2004
Limit cycle-strange attractor competition. Zbl 1141.34323
Criminale, W. O.; Jackson, T. L.; Nelson, P. W.
2004
Mathematical analysis of delay differential equation models of HIV-1 infection. Zbl 0992.92035
Nelson, Patrick W.; Perelson, Alan S.
2002
Traveling-wave solutions of the diffusively corrected kinematic-wave model. Zbl 0994.90031
Nelson, P.
2002
Modeling viral infections. Zbl 1025.92010
Perelson, Alan S.; Nelson, Patrick W.
2002
A model of HIV-1 pathogenesis that includes an intracellular delay. Zbl 0942.92017
Nelson, Patrick W.; Murray, James D.; Perelson, Alan S.
2000
Mathematical analysis of HIV-1 dynamics in vivo. Zbl 1078.92502
Perelson, Alan S.; Nelson, Patrick W.
1999
Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing. Zbl 0766.35074
Dat Duc Bui; Nelson, P.
1992
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### Cited by 1,242 Authors

 41 Elaiw, Ahmed M. 20 Rong, Libin 18 Song, Xinyu 17 Wang, Jinliang 17 Wang, Xia 16 Xu, Rui 13 Ma, Wanbiao 13 Perelson, Alan S. 12 Alshamrani, Noura H. 12 Jiang, Daqing 12 Takeuchi, Yasuhiro 12 Wang, Yan 12 Wu, Hulin 11 Li, Michael Yi 11 Shu, Hongying 10 Huang, Yangxin 10 Liu, Shengqiang 9 Banks, Harvey Thomas 9 Browne, Cameron J. 9 Misra, Arvind Kumar 8 Gumel, Abba B. 8 Li, Xuezhi 7 Alshaikh, Matuka A. 7 Bortz, David M. 7 Ciupe, Stanca M. 7 Hattaf, Khalid 7 Hayat, Tasawar 7 Nelson, Patrick W. 7 Pitchaimani, M. 7 Wang, Kaifa 7 Wang, Shaoli 7 Zhou, Xueyong 7 Zou, Xingfu 6 Cai, Liming 6 Chen, Yuming 6 Kuniya, Toshikazu 6 Qiu, Zhipeng 6 Tiwari, Pankaj Kumar 6 Wang, Lin 6 Wang, Wendi 6 Wang, Xiaoyan 6 Xiao, Yanni 6 Yang, Junyuan 6 Yousfi, Noura 6 Zhou, Yicang 5 Ali, Nigar 5 Allali, Karam 5 Al-saedi, Ahmed Eid Salem 5 Balasubramaniam, Pagavathigounder 5 Blyuss, Konstantin B. 5 Bocharov, Gennady A. 5 Chandra, Peeyush 5 Cheng, Chang-Yuan 5 Dong, Yueping 5 Huang, Gang 5 Kwon, Hee-Dae 5 Liu, Lishan 5 Liu, Xianning 5 Martcheva, Maia 5 Miao, Hui 5 Pilyugin, Sergei S. 5 Shi, Xiangyun 5 Tian, Xiaohong 5 Vargas-De-León, Cruz 5 Xu, Jinhu 5 Yang, Yu 5 Zaman, Gul 5 Zhou, Jie 4 Adak, Debadatta 4 Ainseba, Bedr’Eddine 4 Angstmann, Christopher N. 4 Bairagi, Nandadulal 4 Băleanu, Dumitru I. 4 Commenges, Daniel 4 De Leenheer, Patrick 4 Guo, Ting 4 Harroudi, Sanaa 4 Heffernan, Jane Marie 4 Henry, Bruce I. 4 Hobiny, Aatef D. 4 Hu, Zhixing 4 Iwami, Shingo 4 Jafelice, Rosana Motta 4 Kajiwara, Tsuyoshi 4 Kyrychko, Yuliya N. 4 Lang, Jiying 4 Liu, Qun 4 Luo, Jianfeng 4 Miao, Hongyu 4 Nakaoka, Shinji 4 Pankavich, Stephen 4 Ruan, Shigui 4 Sahani, Saroj Kumar 4 Sasaki, Toru 4 Sharomi, Oluwaseun Y. 4 Sipahi, Rifat 4 Srivastava, Prashant Kr. 4 Teng, Zhi-dong 4 Tridane, Abdessamad 4 Verma, Maitri ...and 1,142 more Authors
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### Cited in 165 Serials

 39 Bulletin of Mathematical Biology 39 Applied Mathematics and Computation 35 Journal of Theoretical Biology 32 International Journal of Biomathematics 31 Mathematical Biosciences 31 Mathematical Biosciences and Engineering 28 Discrete and Continuous Dynamical Systems. Series B 26 Journal of Mathematical Analysis and Applications 23 Journal of Mathematical Biology 23 Discrete Dynamics in Nature and Society 20 Advances in Difference Equations 18 Chaos, Solitons and Fractals 18 Nonlinear Analysis. Real World Applications 16 Journal of Biological Dynamics 14 Mathematical Methods in the Applied Sciences 14 Mathematics and Computers in Simulation 14 Applied Mathematical Modelling 14 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14 Journal of Applied Mathematics and Computing 13 Journal of the Franklin Institute 12 Mathematical and Computer Modelling 11 Communications in Nonlinear Science and Numerical Simulation 10 Automatica 10 Journal of Computational and Applied Mathematics 10 Computational and Applied Mathematics 10 Differential Equations and Dynamical Systems 10 Abstract and Applied Analysis 8 Physica A 8 Computational & Mathematical Methods in Medicine 7 Computers & Mathematics with Applications 7 Journal of Biological Systems 7 Mathematical Modelling of Natural Phenomena 6 Nonlinear Dynamics 6 Nonlinear Analysis. Modelling and Control 5 International Journal of Control 5 International Journal of Computer Mathematics 5 Complexity 5 The Annals of Applied Statistics 4 International Journal of Robust and Nonlinear Control 4 Journal of Nonlinear Science 4 Journal of Inverse and Ill-Posed Problems 4 Mathematical Problems in Engineering 4 Boundary Value Problems 4 International Journal of Applied and Computational Mathematics 3 Applicable Analysis 3 Biometrics 3 Statistics & Probability Letters 3 SIAM Journal on Applied Mathematics 3 Journal of Vibration and Control 3 Journal of Applied Statistics 3 Journal of Systems Science and Complexity 3 Discrete and Continuous Dynamical Systems. Series S 3 Journal of Applied Analysis and Computation 2 Biometrical Journal 2 Journal of Statistical Planning and Inference 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Ricerche di Matematica 2 SIAM Journal on Control and Optimization 2 Theoretical Population Biology 2 Optimal Control Applications & Methods 2 Stochastic Analysis and Applications 2 Acta Mathematicae Applicatae Sinica. English Series 2 Applied Mathematics Letters 2 International Journal of Adaptive Control and Signal Processing 2 Computational Statistics and Data Analysis 2 Journal of Dynamics and Differential Equations 2 Journal of the Egyptian Mathematical Society 2 Journal of Difference Equations and Applications 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Discrete and Continuous Dynamical Systems 2 Arab Journal of Mathematical Sciences 2 Journal of Mathematical Chemistry 2 Chaos 2 International Journal of Applied Mathematics and Computer Science 2 Journal of Applied Mathematics 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Communications on Pure and Applied Analysis 2 Statistical Methods in Medical Research 2 Applications and Applied Mathematics 2 Journal of Nonlinear Science and Applications 2 International Journal of Differential Equations 2 ISRN Biomathematics 2 Cogent Mathematics 2 AIMS Mathematics 1 Acta Mechanica 1 Archive for Rational Mechanics and Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Indian Journal of Pure & Applied Mathematics 1 International Journal of Systems Science 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 The Annals of Statistics 1 Information Sciences 1 Journal of the American Statistical Association 1 Studies in Applied Mathematics 1 Systems & Control Letters 1 Journal of Time Series Analysis 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Applicandae Mathematicae ...and 65 more Serials
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### Cited in 37 Fields

 669 Biology and other natural sciences (92-XX) 418 Ordinary differential equations (34-XX) 123 Dynamical systems and ergodic theory (37-XX) 89 Systems theory; control (93-XX) 79 Numerical analysis (65-XX) 74 Partial differential equations (35-XX) 41 Statistics (62-XX) 35 Calculus of variations and optimal control; optimization (49-XX) 23 Probability theory and stochastic processes (60-XX) 12 Computer science (68-XX) 10 Integral equations (45-XX) 10 Operator theory (47-XX) 9 Real functions (26-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Difference and functional equations (39-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Operations research, mathematical programming (90-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Special functions (33-XX) 3 General and overarching topics; collections (00-XX) 3 Approximations and expansions (41-XX) 3 Mechanics of particles and systems (70-XX) 3 Fluid mechanics (76-XX) 2 Combinatorics (05-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)