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Modeling group dynamics of phototaxis: From particle systems to PDEs
1.  Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742, United States 
2.  Department of Mathematics, Stanford University, Stanford, CA 943052125, United States 
[1] 
SeungYeal Ha, Doron Levy. Particle, kinetic and fluid models for phototaxis. Discrete & Continuous Dynamical Systems  B, 2009, 12 (1) : 77108. doi: 10.3934/dcdsb.2009.12.77 
[2] 
Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of some particle systems with twobody interactions and of the dislocation dynamics. Discrete & Continuous Dynamical Systems  A, 2009, 23 (3) : 785826. doi: 10.3934/dcds.2009.23.785 
[3] 
Nathan GlattHoltz, Mohammed Ziane. Singular perturbation systems with stochastic forcing and the renormalization group method. Discrete & Continuous Dynamical Systems  A, 2010, 26 (4) : 12411268. doi: 10.3934/dcds.2010.26.1241 
[4] 
MirosŁaw Lachowicz, Tatiana Ryabukha. Equilibrium solutions for microscopic stochastic systems in population dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 777786. doi: 10.3934/mbe.2013.10.777 
[5] 
P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of hostparasite systems. Global analysis. Discrete & Continuous Dynamical Systems  B, 2007, 8 (1) : 117. doi: 10.3934/dcdsb.2007.8.1 
[6] 
David Cowan. Rigid particle systems and their billiard models. Discrete & Continuous Dynamical Systems  A, 2008, 22 (1&2) : 111130. doi: 10.3934/dcds.2008.22.111 
[7] 
Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic & Related Models, 2008, 1 (4) : 557572. doi: 10.3934/krm.2008.1.557 
[8] 
Lei Yang, Lianzhang Bao. Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020154 
[9] 
Matteo Petrera, Yuri B. Suris. Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor. Journal of Computational Dynamics, 2019, 6 (2) : 401408. doi: 10.3934/jcd.2019020 
[10] 
Felix X.F. Ye, Hong Qian. Stochastic dynamics Ⅱ: Finite random dynamical systems, linear representation, and entropy production. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 43414366. doi: 10.3934/dcdsb.2019122 
[11] 
Jacques Demongeot, Dan Istrate, Hajer Khlaifi, Lucile Mégret, Carla Taramasco, René Thomas. From conservative to dissipative nonlinear differential systems. An application to the cardiorespiratory regulation. Discrete & Continuous Dynamical Systems  S, 2020, 13 (8) : 21212134. doi: 10.3934/dcdss.2020181 
[12] 
Denis de Carvalho Braga, Luis Fernando Mello, Carmen Rocşoreanu, Mihaela Sterpu. Lyapunov coefficients for nonsymmetrically coupled identical dynamical systems. Application to coupled advertising models. Discrete & Continuous Dynamical Systems  B, 2009, 11 (3) : 785803. doi: 10.3934/dcdsb.2009.11.785 
[13] 
Susanna Terracini, Juncheng Wei. DCDSA Special Volume Qualitative properties of solutions of nonlinear elliptic equations and systems. Preface. Discrete & Continuous Dynamical Systems  A, 2014, 34 (6) : iii. doi: 10.3934/dcds.2014.34.6i 
[14] 
Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reactiondiffusionadvection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 23572376. doi: 10.3934/cpaa.2017116 
[15] 
Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reactiondiffusionadvection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285317. doi: 10.3934/cpaa.2018017 
[16] 
Eliot Fried. New insights into the classical mechanics of particle systems. Discrete & Continuous Dynamical Systems  A, 2010, 28 (4) : 14691504. doi: 10.3934/dcds.2010.28.1469 
[17] 
Lianzhang Bao, Wenxian Shen. Logistic type attractionrepulsion chemotaxis systems with a free boundary or unbounded boundary. I. Asymptotic dynamics in fixed unbounded domain. Discrete & Continuous Dynamical Systems  A, 2020, 40 (2) : 11071130. doi: 10.3934/dcds.2020072 
[18] 
Monica Marras, Stella VernierPiro, Giuseppe Viglialoro. Decay in chemotaxis systems with a logistic term. Discrete & Continuous Dynamical Systems  S, 2020, 13 (2) : 257268. doi: 10.3934/dcdss.2020014 
[19] 
Lee DeVille, Nicole Riemer, Matthew West. Convergence of a generalized Weighted Flow Algorithm for stochastic particle coagulation. Journal of Computational Dynamics, 2019, 6 (1) : 6994. doi: 10.3934/jcd.2019003 
[20] 
Michele Gianfelice, Marco Isopi. On the location of the 1particle branch of the spectrum of the disordered stochastic Ising model. Networks & Heterogeneous Media, 2011, 6 (1) : 127144. doi: 10.3934/nhm.2011.6.127 
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