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Author ID: bodnar.marek Recent zbMATH articles by "Bodnar, Marek"
Published as: Bodnar, Marek; Bodnar, M.
Documents Indexed: 57 Publications since 2000, including 1 Additional arXiv Preprint
Co-Authors: 28 Co-Authors with 48 Joint Publications
234 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

43 Publications have been cited 350 times in 209 Documents Cited by Year
An integro-differential equation arising as a limit of individual cell-based models. Zbl 1089.45002
Bodnar, M.; Velazquez, J. J. L.
61
2006
Time delays in proliferation process for solid avascular tumour. Zbl 1046.92026
Foryś, U.; Bodnar, M.
55
2003
The nonnegativity of solutions to delay differential equations. Zbl 0958.34049
Bodnar, M.
49
2000
Derivation of macroscopic equations for individual cell-based models: a formal approach. Zbl 1074.60101
Bodnar, M.; Velazquez, J. J. L.
37
2005
Time delay in necrotic core formation. Zbl 1115.34078
Bodnar, Marek; Foryś, Urszula
37
2005
Time delays in regulatory apoptosis for solid avascular tumour. Zbl 1047.92025
Foryś, U.; Bodnar, M.
25
2003
Stochastic models of gene expression with delayed degradation. Zbl 1225.92018
Miękisz, Jacek; Poleszczuk, Jan; Bodnar, Marek; Foryś, Urszula
17
2011
Three types of simple DDEs describing tumor growth. Zbl 1151.92015
Bodnar, Marek; Foryś, Urszula
16
2007
Mathematical modelling of immune reaction against gliomas: sensitivity analysis and influence of delays. Zbl 1317.92040
Piotrowska, Monika Joanna; Bodnar, Marek; Poleszczuk, Jan; Foryś, Urszula
15
2013
Stability of delay induced oscillations in gene expression of Hes1 protein model. Zbl 1327.92030
Bodnar, Marek; Bartłomiejczyk, Agnieszka
12
2012
Analysis of biochemical reactions models with delays. Zbl 1205.92030
Bodnar, Marek; Foryś, Urszula; Poleszczuk, Jan
12
2011
Stability analysis of the family of tumour angiogenesis models with distributed time delays. Zbl 1467.92087
Bodnar, Marek; Piotrowska, Monika Joanna
11
2016
Delay can stabilize: love affairs dynamics. Zbl 1311.91161
Bielczyk, Natalia; Bodnar, Marek; Foryś, Urszula
11
2012
A model of immune system with time-dependent immune reactivity. Zbl 1166.34042
Bodnar, M.; Foryś, U.
9
2009
Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model. Zbl 1510.92102
Piotrowska, Monika Joanna; Bodnar, Marek
9
2018
Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. Zbl 1275.35123
Bodnar, M.; Velázquez, J. J. L.
9
2013
New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model. Zbl 1259.34011
Poleszczuk, Jan; Bodnar, Marek; Foryś, Urszula
9
2011
Periodic dynamics in a model of immune system. Zbl 1007.34067
Bodnar, Marek; Foryś, Urszula
8
2000
A modified van der Pol equation with delay in a description of the heart action. Zbl 1309.93076
Zduniak, Beata; Bodnar, Marek; Foryś, Urszula
8
2014
Logistic type equations with discrete delay and quasi-periodic suppression rate. Zbl 1261.92044
Bodnar, Marek; Foryś, Urszula; Piotrowska, Monika J.
8
2013
A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications. Zbl 1377.92043
Bogdańska, M. U.; Bodnar, M.; Belmonte-Beitia, J.; Murek, M.; Schucht, P.; Beck, J.; Pérez-García, V. M.
7
2017
Angiogenesis model with carrying capacity depending on vessel density. Zbl 1369.92013
Bodnar, Marek; Foryś, Urszula
7
2009
Global stability and the Hopf bifurcation for some class of delay differential equations. Zbl 1151.34058
Bodnar, Marek; Foryś, Urszula
6
2008
Dynamic oligopoly with sticky prices: off-steady-state analysis. Zbl 1348.91208
Wiszniewska-Matyszkiel, Agnieszka; Bodnar, Marek; Mirota, Fryderyk
6
2015
General model of a cascade of reactions with time delays: global stability analysis. Zbl 1330.34121
Bodnar, Marek
6
2015
Asymptotic dynamics of some \(t\)-periodic one-dimensional model with application to prostate cancer immunotherapy. Zbl 1360.92055
Foryś, U.; Bodnar, M.; Kogan, Y.
5
2016
Existence and stability of oscillating solutions for a class of delay differential equations. Zbl 1280.34071
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula
5
2013
Model of tumour angiogenesis – analysis of stability with respect to delays. Zbl 1259.34055
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula; Nizińska, Ewa
5
2013
Behaviour of solutions to Marchuk’s model depending on a time delay. Zbl 0947.92015
Bodnar, Marek; Foryś, Urszula
4
2000
Model of AIDS-related tumour with time delay. Zbl 1180.34093
Bodnar, Marek; Foryś, Urszula; Szymańska, Zuzanna
4
2009
Negativity of delayed induced oscillations in a simple linear DDE. Zbl 1218.34079
Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan
4
2011
Gompertz model with delays and treatment: mathematical analysis. Zbl 1268.92056
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula
4
2013
A simple model of carcinogenic mutations with time delay and diffusion. Zbl 1268.92068
Piotrowska, Monika Joanna; Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan
4
2013
Logistic equation with treatment function and discrete delays. Zbl 1409.92122
Piotrowska, Monika Joanna; Bodnar, Marek
3
2014
Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy. Zbl 1464.92122
Bodnar, Marek; Vela Pérez, María
3
2019
Three-player games with strategy-dependent time delays. Zbl 1461.91006
Bodnar, Marek; Miȩkisz, Jacek; Vardanyan, Raffi
3
2020
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics. Zbl 1176.92024
Bodnar, Marek; Foryś, Urszula
3
2009
Mathematical analysis of a generalised p53-Mdm2 protein gene expression model. Zbl 1427.34092
Piotrowska, Monika J.; Bartłomiejczyk, Agnieszka; Bodnar, Marek
3
2018
Delays do not cause oscillations in a corrected model of humoral mediated immune response. Zbl 1410.92031
Bodnar, Marek; Foryś, Urszula
2
2016
About a generalized model of lymphoma. Zbl 1227.92019
Chrobak, J. M.; Bodnar, M.; Herrero, H.
2
2012
Mathematical analysis of a generalised model of chemotherapy for low grade gliomas. Zbl 1422.34146
Bodnar, Marek; Piotrowska, Monika Joanna; Bogdańska, Magdalena Urszula
2
2019
Some remarks on modelling of drug resistance for low grade gliomas. Zbl 1463.34172
Bodnar, Marek; Foryś, Urszula
1
2019
Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein. Zbl 1453.34067
Bartłomiejczyk, Agnieszka; Bodnar, Marek
1
2020
Three-player games with strategy-dependent time delays. Zbl 1461.91006
Bodnar, Marek; Miȩkisz, Jacek; Vardanyan, Raffi
3
2020
Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein. Zbl 1453.34067
Bartłomiejczyk, Agnieszka; Bodnar, Marek
1
2020
Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy. Zbl 1464.92122
Bodnar, Marek; Vela Pérez, María
3
2019
Mathematical analysis of a generalised model of chemotherapy for low grade gliomas. Zbl 1422.34146
Bodnar, Marek; Piotrowska, Monika Joanna; Bogdańska, Magdalena Urszula
2
2019
Some remarks on modelling of drug resistance for low grade gliomas. Zbl 1463.34172
Bodnar, Marek; Foryś, Urszula
1
2019
Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model. Zbl 1510.92102
Piotrowska, Monika Joanna; Bodnar, Marek
9
2018
Mathematical analysis of a generalised p53-Mdm2 protein gene expression model. Zbl 1427.34092
Piotrowska, Monika J.; Bartłomiejczyk, Agnieszka; Bodnar, Marek
3
2018
A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications. Zbl 1377.92043
Bogdańska, M. U.; Bodnar, M.; Belmonte-Beitia, J.; Murek, M.; Schucht, P.; Beck, J.; Pérez-García, V. M.
7
2017
Stability analysis of the family of tumour angiogenesis models with distributed time delays. Zbl 1467.92087
Bodnar, Marek; Piotrowska, Monika Joanna
11
2016
Asymptotic dynamics of some \(t\)-periodic one-dimensional model with application to prostate cancer immunotherapy. Zbl 1360.92055
Foryś, U.; Bodnar, M.; Kogan, Y.
5
2016
Delays do not cause oscillations in a corrected model of humoral mediated immune response. Zbl 1410.92031
Bodnar, Marek; Foryś, Urszula
2
2016
Dynamic oligopoly with sticky prices: off-steady-state analysis. Zbl 1348.91208
Wiszniewska-Matyszkiel, Agnieszka; Bodnar, Marek; Mirota, Fryderyk
6
2015
General model of a cascade of reactions with time delays: global stability analysis. Zbl 1330.34121
Bodnar, Marek
6
2015
A modified van der Pol equation with delay in a description of the heart action. Zbl 1309.93076
Zduniak, Beata; Bodnar, Marek; Foryś, Urszula
8
2014
Logistic equation with treatment function and discrete delays. Zbl 1409.92122
Piotrowska, Monika Joanna; Bodnar, Marek
3
2014
Mathematical modelling of immune reaction against gliomas: sensitivity analysis and influence of delays. Zbl 1317.92040
Piotrowska, Monika Joanna; Bodnar, Marek; Poleszczuk, Jan; Foryś, Urszula
15
2013
Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. Zbl 1275.35123
Bodnar, M.; Velázquez, J. J. L.
9
2013
Logistic type equations with discrete delay and quasi-periodic suppression rate. Zbl 1261.92044
Bodnar, Marek; Foryś, Urszula; Piotrowska, Monika J.
8
2013
Existence and stability of oscillating solutions for a class of delay differential equations. Zbl 1280.34071
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula
5
2013
Model of tumour angiogenesis – analysis of stability with respect to delays. Zbl 1259.34055
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula; Nizińska, Ewa
5
2013
Gompertz model with delays and treatment: mathematical analysis. Zbl 1268.92056
Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula
4
2013
A simple model of carcinogenic mutations with time delay and diffusion. Zbl 1268.92068
Piotrowska, Monika Joanna; Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan
4
2013
Stability of delay induced oscillations in gene expression of Hes1 protein model. Zbl 1327.92030
Bodnar, Marek; Bartłomiejczyk, Agnieszka
12
2012
Delay can stabilize: love affairs dynamics. Zbl 1311.91161
Bielczyk, Natalia; Bodnar, Marek; Foryś, Urszula
11
2012
About a generalized model of lymphoma. Zbl 1227.92019
Chrobak, J. M.; Bodnar, M.; Herrero, H.
2
2012
Stochastic models of gene expression with delayed degradation. Zbl 1225.92018
Miękisz, Jacek; Poleszczuk, Jan; Bodnar, Marek; Foryś, Urszula
17
2011
Analysis of biochemical reactions models with delays. Zbl 1205.92030
Bodnar, Marek; Foryś, Urszula; Poleszczuk, Jan
12
2011
New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model. Zbl 1259.34011
Poleszczuk, Jan; Bodnar, Marek; Foryś, Urszula
9
2011
Negativity of delayed induced oscillations in a simple linear DDE. Zbl 1218.34079
Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan
4
2011
A model of immune system with time-dependent immune reactivity. Zbl 1166.34042
Bodnar, M.; Foryś, U.
9
2009
Angiogenesis model with carrying capacity depending on vessel density. Zbl 1369.92013
Bodnar, Marek; Foryś, Urszula
7
2009
Model of AIDS-related tumour with time delay. Zbl 1180.34093
Bodnar, Marek; Foryś, Urszula; Szymańska, Zuzanna
4
2009
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics. Zbl 1176.92024
Bodnar, Marek; Foryś, Urszula
3
2009
Global stability and the Hopf bifurcation for some class of delay differential equations. Zbl 1151.34058
Bodnar, Marek; Foryś, Urszula
6
2008
Three types of simple DDEs describing tumor growth. Zbl 1151.92015
Bodnar, Marek; Foryś, Urszula
16
2007
An integro-differential equation arising as a limit of individual cell-based models. Zbl 1089.45002
Bodnar, M.; Velazquez, J. J. L.
61
2006
Derivation of macroscopic equations for individual cell-based models: a formal approach. Zbl 1074.60101
Bodnar, M.; Velazquez, J. J. L.
37
2005
Time delay in necrotic core formation. Zbl 1115.34078
Bodnar, Marek; Foryś, Urszula
37
2005
Time delays in proliferation process for solid avascular tumour. Zbl 1046.92026
Foryś, U.; Bodnar, M.
55
2003
Time delays in regulatory apoptosis for solid avascular tumour. Zbl 1047.92025
Foryś, U.; Bodnar, M.
25
2003
The nonnegativity of solutions to delay differential equations. Zbl 0958.34049
Bodnar, M.
49
2000
Periodic dynamics in a model of immune system. Zbl 1007.34067
Bodnar, Marek; Foryś, Urszula
8
2000
Behaviour of solutions to Marchuk’s model depending on a time delay. Zbl 0947.92015
Bodnar, Marek; Foryś, Urszula
4
2000
all top 5

Cited by 318 Authors

36 Xu, Shihe
27 Foryś, Urszula
20 Bodnar, Marek
14 Piotrowska, Monika Joanna
13 Bai, Meng
12 Zhang, Fangwei
7 Khajanchi, Subhas
6 Hu, Bei
4 Bartłomiejczyk, Agnieszka
4 Jackowska-Zduniak, Beata
4 Rihan, Fathalla A.
4 Song, Huijuan
4 Wang, Zejia
3 Banerjee, Sandip
3 Belmonte-Beitia, Juan
3 Huang, Gang
3 Poleszczuk, Jan
3 Wang, Guiyuan
3 Yang, Zhuoqin
3 Zhou, Qinghua
2 Agrawal, Tanuja
2 Bielczyk, Natalia Z.
2 Cao, Jinde
2 Chen, Yinhui
2 Colli, Pierluigi
2 Das, Parthasakha
2 Das, Pritha
2 Das, Samhita
2 Deng, Wei
2 Dong, Yueping
2 Duan, Weilong
2 El-Morshedy, Hassan A.
2 Gao, Qingbin
2 Ghosh, Dibakar
2 Gómez, Héctor J.
2 He, Wenhua
2 Kayan, Şeyma
2 Kogan, Yuri
2 Liao, Xiaofeng
2 Liu, Feng
2 Liu, Yifan
2 Lorenzo, Guillermo
2 Ma, Zhidan
2 Mackey, Michael Charles
2 Marinoschi, Gabriela
2 Merdan, Hüseyin
2 Ning, Lijuan
2 Peng, Mingshu
2 Reali, Alessandro
2 Rocca, Elisabetta
2 Ruiz-Herrera, Alfonso
2 Singh, Rajani
2 Sivaloganathan, Sivabal
2 Su, Dan
2 Takeuchi, Yasuhiro
2 Turcotte, Marc
2 Wiszniewska-Matyszkiel, Agnieszka
2 Xing, Ruixiang
2 Yang, Tao
2 Yu, Jinchen
2 Zduniak, Beata
2 Zeng, Chunhua
2 Zhao, Xiangqing
2 Zhao, Xinyue Evelyn
2 Zhou, Haihua
1 Abdeen, Mostafa A. M.
1 Abdel Rahman, Duaa H.
1 Adom-Konadu, Agnes
1 Agur, Zvia
1 Al Themairi, Asma
1 Alahmadi, Dua M.
1 Alcamí, Arturo Álvarez-Arenas
1 Alidousti, Javad
1 Alkhajeh, A. S.
1 Angus, Simon D.
1 Anokye, Martin
1 Ashi, Hala A.
1 Atamas’, E. I.
1 Atangana, Jacques
1 Attia, Emad R.
1 Bądziul, Dorota
1 Baker, Christopher Thomas Hale
1 Banerjee, Sayanti
1 Bashkirtseva, Irina Adol’fovna
1 Bellomo, Nicola
1 Berezansky, Leonid M.
1 Bianca, Carlo
1 Bishop, D. Timothy
1 Biswas, Santosh
1 Blyuss, Konstantin B.
1 Bodzioch, Mariusz
1 Braverman, Elena
1 Broom, Mark
1 Burbanks, Andrew D.
1 Cai, Jiazhi
1 Cao, Junfei
1 Cerasuolo, Marianna
1 Chaplain, Mark A. J.
1 Cheke, Robert A.
1 Chen, Fengde
...and 218 more Authors
all top 5

Cited in 70 Serials

13 Applied Mathematics and Computation
12 Discrete and Continuous Dynamical Systems. Series B
11 Nonlinear Analysis. Real World Applications
10 Chaos, Solitons and Fractals
8 Journal of Mathematical Analysis and Applications
7 Physica A
7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 Communications in Nonlinear Science and Numerical Simulation
6 Mathematical Methods in the Applied Sciences
6 Journal of Differential Equations
6 Mathematical Biosciences and Engineering
6 Journal of Theoretical Biology
5 Mathematical and Computer Modelling
5 Mathematical Population Studies
5 International Journal of Applied Mathematics and Computer Science
5 International Journal of Biomathematics
4 Journal of Mathematical Biology
4 Boundary Value Problems
4 Computational & Mathematical Methods in Medicine
3 Mathematical Biosciences
3 Bulletin of Mathematical Biology
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Applied Mathematical Modelling
3 Discrete Dynamics in Nature and Society
3 Journal of Applied Mathematics
3 Mathematical Modelling of Natural Phenomena
2 Applicable Analysis
2 Journal of Optimization Theory and Applications
2 Mathematics and Computers in Simulation
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Journal of Nonlinear Science
2 Mathematical Problems in Engineering
2 Nonlinear Dynamics
2 Abstract and Applied Analysis
2 Chaos
2 Mathematica Applicanda
1 Journal of the Franklin Institute
1 Rocky Mountain Journal of Mathematics
1 Automatica
1 The Journal of Mathematical Sociology
1 Systems & Control Letters
1 Operations Research Letters
1 Applied Numerical Mathematics
1 Applied Mathematics Letters
1 International Journal of Computer Mathematics
1 SIAM Journal on Mathematical Analysis
1 Topological Methods in Nonlinear Analysis
1 Computational and Applied Mathematics
1 Complexity
1 Mathematical Methods of Operations Research
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Communications of the Korean Mathematical Society
1 Differential Equations
1 Nonlinear Analysis. Modelling and Control
1 Acta Mathematica Scientia. Series A. (Chinese Edition)
1 Acta Mathematica Scientia. Series B. (English Edition)
1 Journal of Applied Mathematics and Computing
1 Journal of Statistical Mechanics: Theory and Experiment
1 Engineering Optimization
1 Journal of Biological Dynamics
1 Discrete and Continuous Dynamical Systems. Series S
1 International Journal of Differential Equations
1 International Journal of Economic Theory
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Dynamic Games and Applications
1 Computational Methods for Differential Equations
1 International Journal of Applied and Computational Mathematics
1 Journal of Elliptic and Parabolic Equations
1 Applied Mathematics and Nonlinear Sciences
1 Communications on Applied Mathematics and Computation

Citations by Year