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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 
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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 
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Monique Chyba, Benedetto Piccoli. Special issue on mathematical methods in systems biology. Networks and 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 and Continuous Dynamical Systems  B, 2019, 24 (7) : 30893114. doi: 10.3934/dcdsb.2018302 
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Imene Aicha Djebour, Takéo Takahashi, Julie Valein. Feedback stabilization of parabolic systems with input delay. Mathematical Control and Related Fields, 2022, 12 (2) : 405420. doi: 10.3934/mcrf.2021027 
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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 
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Yutian Lei. On the integral systems with negative exponents. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 10391057. doi: 10.3934/dcds.2015.35.1039 
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F. R. Guarguaglini, R. Natalini. Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology. Communications on Pure and Applied Analysis, 2007, 6 (1) : 287309. doi: 10.3934/cpaa.2007.6.287 
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JeChiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 601623. doi: 10.3934/dcds.2008.21.601 
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Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 487515. doi: 10.3934/dcds.2001.7.487 
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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 
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Avner Friedman. Conservation laws in mathematical biology. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 30813097. doi: 10.3934/dcds.2012.32.3081 
[12] 
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 
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Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
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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 and Management Optimization, 2016, 12 (1) : 303315. doi: 10.3934/jimo.2016.12.303 
[15] 
Nguyen H. Sau, Vu N. Phat. LP approach to exponential stabilization of singular linear positive timedelay systems via memory state feedback. Journal of Industrial and Management Optimization, 2018, 14 (2) : 583596. doi: 10.3934/jimo.2017061 
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Biao Zeng. Existence results for fractional impulsive delay feedback control systems with Caputo fractional derivatives. Evolution Equations and Control Theory, 2022, 11 (1) : 239258. doi: 10.3934/eect.2021001 
[17] 
N. Bellomo, A. Bellouquid. From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Discrete and Continuous Dynamical Systems  B, 2004, 4 (1) : 5980. doi: 10.3934/dcdsb.2004.4.59 
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Judith R. Miller, Huihui Zeng. Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology. Discrete and Continuous Dynamical Systems  B, 2011, 16 (3) : 895925. doi: 10.3934/dcdsb.2011.16.895 
[19] 
Avner Friedman. PDE problems arising in mathematical biology. Networks and Heterogeneous Media, 2012, 7 (4) : 691703. doi: 10.3934/nhm.2012.7.691 
[20] 
Benjamin B. Kennedy. A statedependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete and Continuous Dynamical Systems  B, 2013, 18 (6) : 16331650. doi: 10.3934/dcdsb.2013.18.1633 
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