-
Previous Article
Confinement for repulsive-attractive kernels
- DCDS-B Home
- This Issue
- Next Article
Preface to special issue on mathematics of social systems
1. | University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 90095-1555 |
For more information please click the “Full Text” above.
References:
[1] |
A. B. T. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents,, Discrete and Continuous Dynamical Systems, 34 (2014), 1249. Google Scholar |
[2] |
D. Balagué, J. A. Carrillo and Y. Yao, Confinement for repulsive-attractive kernels,, Discrete and Continuous Dynamical Systems, 34 (2014), 1227. Google Scholar |
[3] |
J. Bedrossian and N. Rodríguez, Inhomogeneous Patlak-Keller-Segel models and aggregation equations with nonlinear diffusion in $R^d$,, Discrete and Continuous Dynamical Systems, 34 (2014), 1279. Google Scholar |
[4] |
J. Bedrossian, N. Rodríguez and A. L. Bertozzi, Local and global well-posedness for aggregation equations and Keller-Segel models with degenerate diffusion,, Nonlinearity, 24 (2011), 1683.
doi: 10.1088/0951-7715/24/6/001. |
[5] |
M. Burger, M. Di Francesco, P. A. Markowich and M. T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics,, Discrete and Continuous Dynamical Systems, 34 (2014), 1311. Google Scholar |
[6] |
Y. S. Cho, A. Galstyan, P. J. Brantingham and G. Tita, Latent self-exciting point process model for spatial-temporal networks,, Discrete and Continuous Dynamical Systems, 34 (2014), 1335. Google Scholar |
[7] |
F. Cucker and S. Smale, Emergent behavior in flocks,, IEEE Transactions on Automatic Control, 52 (2007), 852.
doi: 10.1109/TAC.2007.895842. |
[8] |
M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi and L. Chayes, Self-propelled particles with soft-core interactions: patterns, stability and collapse,, Phys. Rev. Lett., 96 (2006).
doi: 10.1103/PhysRevLett.96.104302. |
[9] |
R. Ghosh and K. Lerman, Rethinking Centrality: The role of dynamical processes in social network analysis,, Discrete and Continuous Dynamical Systems, 34 (2014), 1355. Google Scholar |
[10] |
R. A. Hegemann, E. A. Lewis and A. L. Bertozzi, An estimate & Score Algorithm for simultaneous parameter estimation and reconstruction of incomplete data on social networks,, Security Informatics, 2 (): 1.
doi: 10.1186/2190-8532-2-1. |
[11] |
T. Kolokolnikov, H. Sun, D. Uminsky and A. L. Bertozzi, Stability of ring patterns arising from two-dimensional particle interactions,, Phys. Rev. E, 84 (2011).
doi: 10.1103/PhysRevE.84.015203. |
[12] |
T. Kolokolnikov, M. J. Ward and J. Wei, The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime,, Discrete and Continuous Dynamical Systems, 34 (2014), 1373. Google Scholar |
[13] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models,, J. Math. Biol., 45 (2002), 219.
doi: 10.1007/s002850200144. |
[14] |
A. Mackey, T. Kolokolnikov and A. L. Bertozzi, Two-species particle aggregation and stability of co-dimension one solutions,, Discrete and Continuous Dynamical Systems, 34 (2014), 1411. Google Scholar |
[15] |
S. G. McCalla, Paladins as predators: Invasive waves in a spatial evolutionary adversarial game,, Discrete and Continuous Dynamical Systems, 34 (2014), 1437. Google Scholar |
[16] |
M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior,, Math. Models. Meth. Appl. Sci., 18 (2008), 1249.
doi: 10.1142/S0218202508003029. |
[17] |
M. B. Short, A. L. Bertozzi and P. J. Brantingham, Nonlinear patterns in urban crime - hotpsots, bifurcations, and suppression,, SIAM J. Appl. Dyn. Sys., 9 (2010), 462.
doi: 10.1137/090759069. |
[18] |
M. B. Short, P. J. Brantingham, A. L. Bertozzi and G. E. Tita, Dissipation and displacement of hotpsots in reaction-diffusion models of crime,, Proc. Nat. Acad. Sci., 107 (2010), 3961. Google Scholar |
[19] |
M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society,, Phys. Rev. E, 82 (2010).
doi: 10.1103/PhysRevE.82.066114. |
[20] |
M. B. Short, G. O. Mohler, P. J. Brantingham and G. E. Tita, Gang rivalry dynamics via coupled point process networks,, Discrete and Continuous Dynamical Systems, 34 (2014), 1459. Google Scholar |
[21] |
A. Stomakhin, M. B. Short and A. L. Bertozzi, Reconstruction of missing data in social networks based on temporal patterns of interactions,, Inverse Problems, 27 (2011).
doi: 10.1088/0266-5611/27/11/115013. |
[22] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase in a system of self-driven particles,, Phys. Rev. Lett., 75 (1995), 1226. Google Scholar |
[23] |
X.-S. Wang, H. Wang and J. Wu., Traveling waves of diffusive predator-prey systems: Disease outbreak propagation,, Discrete Contin. Dyn. Syst., 32 (2012), 3303.
doi: 10.3934/dcds.2012.32.3303. |
[24] |
J. R. Zipkin, M. B. Short and A. L. Bertozzi, Cops on the dots in a mathematical model of urban crime and police response,, Discrete and Continuous Dynamical Systems, 34 (2014), 1479. Google Scholar |
show all references
References:
[1] |
A. B. T. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents,, Discrete and Continuous Dynamical Systems, 34 (2014), 1249. Google Scholar |
[2] |
D. Balagué, J. A. Carrillo and Y. Yao, Confinement for repulsive-attractive kernels,, Discrete and Continuous Dynamical Systems, 34 (2014), 1227. Google Scholar |
[3] |
J. Bedrossian and N. Rodríguez, Inhomogeneous Patlak-Keller-Segel models and aggregation equations with nonlinear diffusion in $R^d$,, Discrete and Continuous Dynamical Systems, 34 (2014), 1279. Google Scholar |
[4] |
J. Bedrossian, N. Rodríguez and A. L. Bertozzi, Local and global well-posedness for aggregation equations and Keller-Segel models with degenerate diffusion,, Nonlinearity, 24 (2011), 1683.
doi: 10.1088/0951-7715/24/6/001. |
[5] |
M. Burger, M. Di Francesco, P. A. Markowich and M. T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics,, Discrete and Continuous Dynamical Systems, 34 (2014), 1311. Google Scholar |
[6] |
Y. S. Cho, A. Galstyan, P. J. Brantingham and G. Tita, Latent self-exciting point process model for spatial-temporal networks,, Discrete and Continuous Dynamical Systems, 34 (2014), 1335. Google Scholar |
[7] |
F. Cucker and S. Smale, Emergent behavior in flocks,, IEEE Transactions on Automatic Control, 52 (2007), 852.
doi: 10.1109/TAC.2007.895842. |
[8] |
M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi and L. Chayes, Self-propelled particles with soft-core interactions: patterns, stability and collapse,, Phys. Rev. Lett., 96 (2006).
doi: 10.1103/PhysRevLett.96.104302. |
[9] |
R. Ghosh and K. Lerman, Rethinking Centrality: The role of dynamical processes in social network analysis,, Discrete and Continuous Dynamical Systems, 34 (2014), 1355. Google Scholar |
[10] |
R. A. Hegemann, E. A. Lewis and A. L. Bertozzi, An estimate & Score Algorithm for simultaneous parameter estimation and reconstruction of incomplete data on social networks,, Security Informatics, 2 (): 1.
doi: 10.1186/2190-8532-2-1. |
[11] |
T. Kolokolnikov, H. Sun, D. Uminsky and A. L. Bertozzi, Stability of ring patterns arising from two-dimensional particle interactions,, Phys. Rev. E, 84 (2011).
doi: 10.1103/PhysRevE.84.015203. |
[12] |
T. Kolokolnikov, M. J. Ward and J. Wei, The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime,, Discrete and Continuous Dynamical Systems, 34 (2014), 1373. Google Scholar |
[13] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models,, J. Math. Biol., 45 (2002), 219.
doi: 10.1007/s002850200144. |
[14] |
A. Mackey, T. Kolokolnikov and A. L. Bertozzi, Two-species particle aggregation and stability of co-dimension one solutions,, Discrete and Continuous Dynamical Systems, 34 (2014), 1411. Google Scholar |
[15] |
S. G. McCalla, Paladins as predators: Invasive waves in a spatial evolutionary adversarial game,, Discrete and Continuous Dynamical Systems, 34 (2014), 1437. Google Scholar |
[16] |
M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior,, Math. Models. Meth. Appl. Sci., 18 (2008), 1249.
doi: 10.1142/S0218202508003029. |
[17] |
M. B. Short, A. L. Bertozzi and P. J. Brantingham, Nonlinear patterns in urban crime - hotpsots, bifurcations, and suppression,, SIAM J. Appl. Dyn. Sys., 9 (2010), 462.
doi: 10.1137/090759069. |
[18] |
M. B. Short, P. J. Brantingham, A. L. Bertozzi and G. E. Tita, Dissipation and displacement of hotpsots in reaction-diffusion models of crime,, Proc. Nat. Acad. Sci., 107 (2010), 3961. Google Scholar |
[19] |
M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society,, Phys. Rev. E, 82 (2010).
doi: 10.1103/PhysRevE.82.066114. |
[20] |
M. B. Short, G. O. Mohler, P. J. Brantingham and G. E. Tita, Gang rivalry dynamics via coupled point process networks,, Discrete and Continuous Dynamical Systems, 34 (2014), 1459. Google Scholar |
[21] |
A. Stomakhin, M. B. Short and A. L. Bertozzi, Reconstruction of missing data in social networks based on temporal patterns of interactions,, Inverse Problems, 27 (2011).
doi: 10.1088/0266-5611/27/11/115013. |
[22] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase in a system of self-driven particles,, Phys. Rev. Lett., 75 (1995), 1226. Google Scholar |
[23] |
X.-S. Wang, H. Wang and J. Wu., Traveling waves of diffusive predator-prey systems: Disease outbreak propagation,, Discrete Contin. Dyn. Syst., 32 (2012), 3303.
doi: 10.3934/dcds.2012.32.3303. |
[24] |
J. R. Zipkin, M. B. Short and A. L. Bertozzi, Cops on the dots in a mathematical model of urban crime and police response,, Discrete and Continuous Dynamical Systems, 34 (2014), 1479. Google Scholar |
[1] |
Holly Gaff. Preliminary analysis of an agent-based model for a tick-borne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463-473. doi: 10.3934/mbe.2011.8.463 |
[2] |
Peter Rashkov. Remarks on pattern formation in a model for hair follicle spacing. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1555-1572. doi: 10.3934/dcdsb.2015.20.1555 |
[3] |
Rui Peng, Fengqi Yi. On spatiotemporal pattern formation in a diffusive bimolecular model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 217-230. doi: 10.3934/dcdsb.2011.15.217 |
[4] |
Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation. Networks & Heterogeneous Media, 2015, 10 (3) : 527-542. doi: 10.3934/nhm.2015.10.527 |
[5] |
Fengqi Yi, Eamonn A. Gaffney, Sungrim Seirin-Lee. The bifurcation analysis of turing pattern formation induced by delay and diffusion in the Schnakenberg system. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 647-668. doi: 10.3934/dcdsb.2017031 |
[6] |
Kolade M. Owolabi. Numerical analysis and pattern formation process for space-fractional superdiffusive systems. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 543-566. doi: 10.3934/dcdss.2019036 |
[7] |
Weiping Li, Haiyan Wu, Jie Yang. Intelligent recognition algorithm for social network sensitive information based on classification technology. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1385-1398. doi: 10.3934/dcdss.2019095 |
[8] |
Rumi Ghosh, Kristina Lerman. Rethinking centrality: The role of dynamical processes in social network analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1355-1372. doi: 10.3934/dcdsb.2014.19.1355 |
[9] |
R.A. Satnoianu, Philip K. Maini, F.S. Garduno, J.P. Armitage. Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 339-362. doi: 10.3934/dcdsb.2001.1.339 |
[10] |
Guanqi Liu, Yuwen Wang. Pattern formation of a coupled two-cell Schnakenberg model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1051-1062. doi: 10.3934/dcdss.2017056 |
[11] |
Qingyan Shi, Junping Shi, Yongli Song. Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 467-486. doi: 10.3934/dcdsb.2018182 |
[12] |
Pradeep Dubey, Rahul Garg, Bernard De Meyer. Competing for customers in a social network. Journal of Dynamics & Games, 2014, 1 (3) : 377-409. doi: 10.3934/jdg.2014.1.377 |
[13] |
Mark G. Burch, Karly A. Jacobsen, Joseph H. Tien, Grzegorz A. Rempała. Network-based analysis of a small Ebola outbreak. Mathematical Biosciences & Engineering, 2017, 14 (1) : 67-77. doi: 10.3934/mbe.2017005 |
[14] |
V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks & Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621 |
[15] |
Marco Scianna, Luca Munaron. Multiscale model of tumor-derived capillary-like network formation. Networks & Heterogeneous Media, 2011, 6 (4) : 597-624. doi: 10.3934/nhm.2011.6.597 |
[16] |
Yao-Li Chuang, Tom Chou, Maria R. D'Orsogna. A network model of immigration: Enclave formation vs. cultural integration. Networks & Heterogeneous Media, 2019, 14 (1) : 53-77. doi: 10.3934/nhm.2019004 |
[17] |
Wonlyul Ko, Inkyung Ahn. Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction. Communications on Pure & Applied Analysis, 2018, 17 (2) : 375-389. doi: 10.3934/cpaa.2018021 |
[18] |
Xiaoying Wang, Xingfu Zou. Pattern formation of a predator-prey model with the cost of anti-predator behaviors. Mathematical Biosciences & Engineering, 2018, 15 (3) : 775-805. doi: 10.3934/mbe.2018035 |
[19] |
Konstantin Avrachenkov, Giovanni Neglia, Vikas Vikram Singh. Network formation games with teams. Journal of Dynamics & Games, 2016, 3 (4) : 303-318. doi: 10.3934/jdg.2016016 |
[20] |
Gianluca D'Antonio, Paul Macklin, Luigi Preziosi. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix. Mathematical Biosciences & Engineering, 2013, 10 (1) : 75-101. doi: 10.3934/mbe.2013.10.75 |
2018 Impact Factor: 1.008
Tools
Metrics
Other articles
by authors
[Back to Top]