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Onedimensional attractor for a dissipative system with a cylindrical phase space
Global attractivity, I/O monotone smallgain theorems, and biological delay systems
1.  Department of Mathematics, Rutgers University, Piscataway, NJ 088548019, United States, United States 
[1] 
Eugene Kashdan, Dominique Duncan, Andrew Parnell, Heinz Schättler. Mathematical methods in systems biology. Mathematical Biosciences & Engineering, 2016, 13 (6) : iii. doi: 10.3934/mbe.201606i 
[2] 
Monique Chyba, Benedetto Piccoli. Special issue on mathematical methods in systems biology. Networks & Heterogeneous Media, 2019, 14 (1) : ⅰⅱ. doi: 10.3934/nhm.20191i 
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Yoshiaki Muroya, Teresa Faria. Attractivity of saturated equilibria for LotkaVolterra systems with infinite delays and feedback controls. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 30893114. doi: 10.3934/dcdsb.2018302 
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Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe. Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Mathematical Biosciences & Engineering, 2006, 3 (4) : 571582. doi: 10.3934/mbe.2006.3.571 
[5] 
Yutian Lei. On the integral systems with negative exponents. Discrete & Continuous Dynamical Systems  A, 2015, 35 (3) : 10391057. doi: 10.3934/dcds.2015.35.1039 
[6] 
JeChiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete & Continuous Dynamical Systems  A, 2008, 21 (2) : 601623. doi: 10.3934/dcds.2008.21.601 
[7] 
F. R. Guarguaglini, R. Natalini. Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology. Communications on Pure & Applied Analysis, 2007, 6 (1) : 287309. doi: 10.3934/cpaa.2007.6.287 
[8] 
Edward J. Allen. Derivation and computation of discretedelay and continuousdelay SDEs in mathematical biology. Mathematical Biosciences & Engineering, 2014, 11 (3) : 403425. doi: 10.3934/mbe.2014.11.403 
[9] 
Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete & Continuous Dynamical Systems  A, 2001, 7 (3) : 487515. doi: 10.3934/dcds.2001.7.487 
[10] 
Tibor Krisztin. The unstable set of zero and the global attractor for delayed monotone positive feedback. Conference Publications, 2001, 2001 (Special) : 229240. doi: 10.3934/proc.2001.2001.229 
[11] 
Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems  A, 2012, 32 (9) : 30813097. doi: 10.3934/dcds.2012.32.3081 
[12] 
Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
[13] 
Ta T.H. Trang, Vu N. Phat, Adly Samir. Finitetime stabilization and $H_\infty$ control of nonlinear delay systems via output feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 303315. doi: 10.3934/jimo.2016.12.303 
[14] 
Nguyen H. Sau, Vu N. Phat. LP approach to exponential stabilization of singular linear positive timedelay systems via memory state feedback. Journal of Industrial & Management Optimization, 2018, 14 (2) : 583596. doi: 10.3934/jimo.2017061 
[15] 
Benjamin B. Kennedy. A statedependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 16331650. doi: 10.3934/dcdsb.2013.18.1633 
[16] 
Benjamin B. Kennedy. A periodic solution with nonsimple oscillation for an equation with statedependent delay and strictly monotonic negative feedback. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 4766. doi: 10.3934/dcdss.2020003 
[17] 
N. Bellomo, A. Bellouquid. From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 5980. doi: 10.3934/dcdsb.2004.4.59 
[18] 
Judith R. Miller, Huihui Zeng. Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology. Discrete & Continuous Dynamical Systems  B, 2011, 16 (3) : 895925. doi: 10.3934/dcdsb.2011.16.895 
[19] 
Huawen Ye, Honglei Xu. Global stabilization for ballandbeam systems via state and partial state feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 1729. doi: 10.3934/jimo.2016.12.17 
[20] 
Guangliang Zhao, Fuke Wu, George Yin. Feedback controls to ensure global solutions and asymptotic stability of Markovian switching diffusion systems. Mathematical Control & Related Fields, 2015, 5 (2) : 359376. doi: 10.3934/mcrf.2015.5.359 
2018 Impact Factor: 1.143
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