# zbMATH — the first resource for mathematics

## Mierczyński, Janusz

Compute Distance To:
 Author ID: mierczynski.janusz Published as: Mierczyński, Janusz; Mierczyński, J.; Mierczynski, Janusz; Mierczýnski, Janusz External Links: MGP
 Documents Indexed: 47 Publications since 1984, including 1 Book
all top 5

#### Co-Authors

 28 single-authored 12 Shen, Wenxian 1 Balbus, Joanna 1 Banaji, Murad 1 Jiang, Jifa 1 Niu, Lei 1 Novo, Sylvia 1 Obaya, Rafael 1 Poláčik, Peter 1 Ruiz-Herrera, Alfonso 1 Schreiber, Sebastian J. 1 Wang, Yi 1 Zhao, Xiao-Qiang
all top 5

#### Serials

 7 Journal of Differential Equations 6 Colloquium Mathematicum 4 Journal of Mathematical Analysis and Applications 3 Proceedings of the American Mathematical Society 2 Journal of Dynamics and Differential Equations 2 Discrete and Continuous Dynamical Systems. Series B 2 Communications on Pure and Applied Analysis 1 Mathematical Methods in the Applied Sciences 1 Mathematische Annalen 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Differential and Integral Equations 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Applicationes Mathematicae 1 Journal of Difference Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Journal of Evolution Equations 1 Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Nonautonomous Dynamical Systems 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

#### Fields

 30 Dynamical systems and ergodic theory (37-XX) 23 Ordinary differential equations (34-XX) 21 Partial differential equations (35-XX) 10 Biology and other natural sciences (92-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operator theory (47-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX)

#### Citations contained in zbMATH Open

36 Publications have been cited 277 times in 146 Documents Cited by Year
Spectral theory for random and nonautonomous parabolic equations and applications. Zbl 1387.35007
Mierczyński, Janusz; Shen, Wenxian
2008
The $$C^ 1$$ property of carrying simplices for a class of competitive systems of ODEs. Zbl 0804.34048
Mierczýnski, Janusz
1994
Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations. Zbl 1024.35091
Mierczyński, Janusz; Shen, Wenxian
2003
Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding. Zbl 1166.37009
Jiang, Jifa; Mierczyński, Janusz; Wang, Yi
2009
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I: General theory. Zbl 1350.37061
Mierczyński, Janusz; Shen, Wenxian
2013
Lyapunov exponents and asymptotic dynamics in random Kolmogorov models. Zbl 1069.35013
Mierczyński, Janusz; Shen, Wenxian
2004
On smoothness of carrying simplices. Zbl 0912.34037
Mierczynski, Janusz
1999
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems. Zbl 1320.37027
Mierczyński, Janusz; Shen, Wenxian
2013
Kolmogorov vector fields with robustly permanent subsystems. Zbl 1017.34052
Mierczyński, Janusz; Schreiber, Sebastian J.
2002
Strictly cooperative systems with a first integral. Zbl 0657.34033
Mierczyński, Janusz
1987
Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions. Zbl 0877.35052
Mierczyński, Janusz
1997
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Basic properties. Zbl 0982.35079
Mierczyński, Janusz
2000
Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions. Zbl 0921.35064
Mierczyński, Janusz
1998
Uniform persistence for nonautonomous and random parabolic Kolmogorov systems. Zbl 1092.35015
Mierczyński, Janusz; Shen, Wenxian; Zhao, Xiao-Qiang
2004
Global convergence in systems of differential equations arising from chemical reaction networks. Zbl 1264.34065
2013
Time averaging for nonautonomous/random linear parabolic equations. Zbl 1170.35047
Mierczyński, Janusz; Shen, Wenxian
2008
$$P$$-arcs in strongly monotone discrete-time dynamical systems. Zbl 0864.58054
Mierczyński, Janusz
1994
On peaks in carrying simplices. Zbl 0936.34036
Mierczyński, Janusz
1999
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
1989
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. parabolic equations and delay systems. Zbl 1367.37050
Mierczyński, Janusz; Shen, Wenxian
2016
The Faber-Krahn inequality for random/nonautonomous parabolic equations. Zbl 1194.35520
Mierczyński, Janusz; Shen, Wenxian
2005
Instability in linear cooperative systems of ordinary differential equations. Zbl 1372.34028
Mierczyński, Janusz
2017
Smoothness of unordered curves in two-dimensional strongly competitive systems. Zbl 1005.34042
Mierczyński, Janusz
1999
The $$C^1$$ property of convex carrying simplices for three-dimensional competitive maps. Zbl 1401.37033
Mierczyński, Janusz
2018
Linearization and invariant manifolds on the carrying simplex for competitive maps. Zbl 1436.37041
Mierczyński, Janusz; Niu, Lei; Ruiz-Herrera, Alfonso
2019
Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs. Zbl 1311.34123
Mierczyński, Janusz
2015
Spectral theory for forward nonautonomous parabolic equations and applications. Zbl 1274.35253
Mierczyński, Janusz; Shen, Wenxian
2012
Persistence in forward nonautonomous competitive systems of parabolic equations. Zbl 1239.35059
Mierczyński, Janusz; Shen, Wenxian
2011
Time-averaging and permanence in nonautonomous competitive systems of PDEs via Vance-Coddington estimates. Zbl 1251.35035
Balbus, Joanna; Mierczyński, Janusz
2012
On monotone trajectories. Zbl 0737.58010
Mierczyński, Janusz
1991
A class of strongly cooperative systems without compactness. Zbl 0737.34032
Mierczyński, Janusz
1991
Estimates for principal Lyapunov exponents: a survey. Zbl 1316.34004
Mierczyński, Janusz
2014
Uniqueness for a class of cooperative systems of ordinary differential equations. Zbl 0831.34001
Mierczyński, Janusz
1994
On a generic behavior in strongly cooperative differential equations. Zbl 0705.34027
Mierczyński, J.
1990
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case. Zbl 0999.35063
Mierczyński, Janusz
2001
The $$C^1$$ property of convex carrying simplices for competitive maps. Zbl 1441.37030
Mierczyński, Janusz
2020
The $$C^1$$ property of convex carrying simplices for competitive maps. Zbl 1441.37030
Mierczyński, Janusz
2020
Linearization and invariant manifolds on the carrying simplex for competitive maps. Zbl 1436.37041
Mierczyński, Janusz; Niu, Lei; Ruiz-Herrera, Alfonso
2019
The $$C^1$$ property of convex carrying simplices for three-dimensional competitive maps. Zbl 1401.37033
Mierczyński, Janusz
2018
Instability in linear cooperative systems of ordinary differential equations. Zbl 1372.34028
Mierczyński, Janusz
2017
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. parabolic equations and delay systems. Zbl 1367.37050
Mierczyński, Janusz; Shen, Wenxian
2016
Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs. Zbl 1311.34123
Mierczyński, Janusz
2015
Estimates for principal Lyapunov exponents: a survey. Zbl 1316.34004
Mierczyński, Janusz
2014
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I: General theory. Zbl 1350.37061
Mierczyński, Janusz; Shen, Wenxian
2013
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems. Zbl 1320.37027
Mierczyński, Janusz; Shen, Wenxian
2013
Global convergence in systems of differential equations arising from chemical reaction networks. Zbl 1264.34065
2013
Spectral theory for forward nonautonomous parabolic equations and applications. Zbl 1274.35253
Mierczyński, Janusz; Shen, Wenxian
2012
Time-averaging and permanence in nonautonomous competitive systems of PDEs via Vance-Coddington estimates. Zbl 1251.35035
Balbus, Joanna; Mierczyński, Janusz
2012
Persistence in forward nonautonomous competitive systems of parabolic equations. Zbl 1239.35059
Mierczyński, Janusz; Shen, Wenxian
2011
Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding. Zbl 1166.37009
Jiang, Jifa; Mierczyński, Janusz; Wang, Yi
2009
Spectral theory for random and nonautonomous parabolic equations and applications. Zbl 1387.35007
Mierczyński, Janusz; Shen, Wenxian
2008
Time averaging for nonautonomous/random linear parabolic equations. Zbl 1170.35047
Mierczyński, Janusz; Shen, Wenxian
2008
The Faber-Krahn inequality for random/nonautonomous parabolic equations. Zbl 1194.35520
Mierczyński, Janusz; Shen, Wenxian
2005
Lyapunov exponents and asymptotic dynamics in random Kolmogorov models. Zbl 1069.35013
Mierczyński, Janusz; Shen, Wenxian
2004
Uniform persistence for nonautonomous and random parabolic Kolmogorov systems. Zbl 1092.35015
Mierczyński, Janusz; Shen, Wenxian; Zhao, Xiao-Qiang
2004
Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations. Zbl 1024.35091
Mierczyński, Janusz; Shen, Wenxian
2003
Kolmogorov vector fields with robustly permanent subsystems. Zbl 1017.34052
Mierczyński, Janusz; Schreiber, Sebastian J.
2002
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case. Zbl 0999.35063
Mierczyński, Janusz
2001
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Basic properties. Zbl 0982.35079
Mierczyński, Janusz
2000
On smoothness of carrying simplices. Zbl 0912.34037
Mierczynski, Janusz
1999
On peaks in carrying simplices. Zbl 0936.34036
Mierczyński, Janusz
1999
Smoothness of unordered curves in two-dimensional strongly competitive systems. Zbl 1005.34042
Mierczyński, Janusz
1999
Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions. Zbl 0921.35064
Mierczyński, Janusz
1998
Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions. Zbl 0877.35052
Mierczyński, Janusz
1997
The $$C^ 1$$ property of carrying simplices for a class of competitive systems of ODEs. Zbl 0804.34048
Mierczýnski, Janusz
1994
$$P$$-arcs in strongly monotone discrete-time dynamical systems. Zbl 0864.58054
Mierczyński, Janusz
1994
Uniqueness for a class of cooperative systems of ordinary differential equations. Zbl 0831.34001
Mierczyński, Janusz
1994
On monotone trajectories. Zbl 0737.58010
Mierczyński, Janusz
1991
A class of strongly cooperative systems without compactness. Zbl 0737.34032
Mierczyński, Janusz
1991
On a generic behavior in strongly cooperative differential equations. Zbl 0705.34027
Mierczyński, J.
1990
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
1989
Strictly cooperative systems with a first integral. Zbl 0657.34033
Mierczyński, Janusz
1987
all top 5

#### Cited by 145 Authors

 19 Mierczyński, Janusz 18 Shen, Wenxian 15 Wang, Yi 10 Jiang, Jifa 9 Gyllenberg, Mats 8 Niu, Lei 7 Baigent, Stephen A. 7 Obaya, Rafael 6 Hou, Zhanyuan 6 Sanz, Ana M. 5 Poláčik, Peter 5 Schreiber, Sebastian J. 4 Húska, Juraj 4 Ruiz-Herrera, Alfonso 4 Yan, Ping 4 Zhou, Dun 3 Banaji, Murad 3 Benaïm, Michel 3 Lian, Zeng 2 Ahmad, Shair 2 Angeli, David 2 Balbus, Joanna 2 Bao, Xiongxiong 2 Cantrell, Robert Stephen 2 Ching, Atheeta 2 Dai, Guowei 2 De Leenheer, Patrick 2 Feng, Lirui 2 Hirsch, Morris W. 2 Hu, Hongxiao 2 Lam, King-Yeung 2 Langa, Jose’ Antonio 2 Liang, Xing 2 Lu, Kening 2 Matano, Hiroshi 2 Neamţu, Alexandra 2 Ogiwara, Toshiko 2 Seymenoglu, Belgin 2 Sontag, Eduardo D. 2 Strickler, Edouard 2 Teng, Zhi-dong 2 Tineo, Antonio R. 2 Wu, Jianhong 2 Zeeman, Mary Lou 1 Aeyels, Dirk 1 Alexeeva, Tatyana Anatolyevna 1 Babaei, Esmaeil 1 Bao, Lianzhang 1 Bar-Shalom, Eyal 1 Belghith, Safya 1 Blumenthal, Alex 1 Brunner, James D. 1 Burbanks, Andrew D. 1 Calzada, Juan A. 1 Cao, Feng 1 Cao, Xiaofei 1 Cao, Yongluo 1 Caraballo Garrido, Tomás 1 Chen, Guangye 1 Chukwu, Ethelbert Nwakuche 1 Conradi, Carsten 1 Craciun, Gheorghe 1 Doan, Thai Son 1 El Ghordaf, J. 1 Evstigneev, Igor V. 1 Fang, Chun 1 Fathallah-Shaykh, Hassan M. 1 Freiji, Abraham 1 Fu, Hongbo 1 Gorban, Alexander N. 1 Gritli, Hassene 1 Hbid, Moulay Lhassan 1 Hening, Alexandru 1 Hilhorst, Danielle 1 Hofbauer, Josef 1 Horan, Joseph 1 Jara, Juan C. 1 Jiang, Haijun 1 Klika, Václav 1 Krause, Andrew L. 1 Kühn, Christian 1 Kulenović, Mustafa R. S. 1 Kuznetsov, Nikolay Vladimirovich 1 Lazer, Alan C. 1 Leonov, Gennadiĭ Alekseevich 1 Li, Fei 1 Li, Wan-Tong 1 Liu, Jicheng 1 Liu, Qiang 1 Liz, Eduardo 1 Ma, Ruyun 1 Mao, Wei 1 Mao, Xuerong 1 Margaliot, Michael 1 Meng, Xinzhu 1 Merino, Orlando 1 Morris, Ian D. 1 Nadin, Grégoire 1 Nguyen, Dang Hai 1 Niu, Lin ...and 45 more Authors
all top 5

#### Cited in 50 Serials

 31 Journal of Differential Equations 7 Journal of Mathematical Analysis and Applications 7 Proceedings of the American Mathematical Society 7 Journal of Difference Equations and Applications 7 Nonlinear Analysis. Real World Applications 7 Discrete and Continuous Dynamical Systems. Series B 6 Journal of Dynamics and Differential Equations 6 Discrete and Continuous Dynamical Systems 5 Journal of Mathematical Biology 5 Nonlinearity 5 Applied Mathematics and Computation 5 Transactions of the American Mathematical Society 2 Archive for Rational Mechanics and Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Acta Applicandae Mathematicae 2 Physica D 2 The Annals of Applied Probability 2 SIAM Journal on Mathematical Analysis 2 Dynamical Systems 2 SIAM Journal on Applied Dynamical Systems 2 Journal of Biological Dynamics 2 Discrete and Continuous Dynamical Systems. Series S 1 Communications in Mathematical Physics 1 Bulletin of Mathematical Biology 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Automatica 1 Memoirs of the American Mathematical Society 1 Siberian Mathematical Journal 1 Ergodic Theory and Dynamical Systems 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Applied Mathematics Letters 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 Journal of Mathematical Chemistry 1 Differential Equations and Dynamical Systems 1 Nonlinear Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Evolution Equations 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 Advances in Difference Equations 1 Computational & Mathematical Methods in Medicine 1 Nonautonomous Dynamical Systems 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

#### Cited in 25 Fields

 81 Dynamical systems and ergodic theory (37-XX) 64 Biology and other natural sciences (92-XX) 44 Ordinary differential equations (34-XX) 44 Partial differential equations (35-XX) 13 Probability theory and stochastic processes (60-XX) 10 Difference and functional equations (39-XX) 7 Operator theory (47-XX) 5 Systems theory; control (93-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Integral equations (45-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Functional analysis (46-XX) 2 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)