-
Previous Article
A semi-Lagrangian scheme for a degenerate second order mean field game system
- DCDS Home
- This Issue
-
Next Article
Global propagation of singularities for time dependent Hamilton-Jacobi equations
A nonlinear model of opinion formation on the sphere
1. | Équipe M2N - EA 7340, Conservatoire National des Arts et Métiers, Paris, France |
2. | Dipartimento di Matematica e Fisica, Università degli studi di Roma Tre, Rome, Italy |
3. | Department of Mathematical Sciences & Center for Computational and Integrative Biology, Rutgers University, Camden, NJ |
References:
[1] |
L. Behera and F. Schweitzer, On spatial consensus formation: Is the sznajd model different from a voter model?, International Journal of Modern Physics C, 14 (2003), 1331-1354.
doi: 10.1142/S0129183103005467. |
[2] |
V. D. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, 48 (2010), 5214-5240.
doi: 10.1137/090766188. |
[3] |
G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Advances in Complex Systems, 3 (2000), 87-98.
doi: 10.1142/S0219525900000078. |
[4] |
R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence models, analysis, and simulation,, Journal of Artificial Societies and Social Simulation, 5 ().
|
[5] |
J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national academy of sciences, 79 (1982), 2554-2558.
doi: 10.1073/pnas.79.8.2554. |
[6] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, Automatic Control, IEEE Transactions on, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[7] |
Y. Kuramoto, Cooperative dynamics of oscillator community a study based on lattice of rings, Progress of Theoretical Physics Supplement, 79 (1984), 223-240.
doi: 10.1143/PTPS.79.223. |
[8] |
J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, International Journal of Modern Physics C, 18 (2007), 1819-1838.
doi: 10.1142/S0129183107011789. |
[9] |
L. Moreau, Stability of continuous-time distributed consensus algorithms, in Decision and Control, 2004. CDC. 43rd IEEE Conference on, vol. 4, IEEE, (2004), 3998-4003.
doi: 10.1109/CDC.2004.1429377. |
[10] |
L. Moreau, Stability of multiagent systems with time-dependent communication links, Automatic Control, IEEE Transactions on, 50 (2005), 169-182.
doi: 10.1109/TAC.2004.841888. |
[11] |
M. C. Nisbet, The competition for worldviews: Values, information, and public support for stem cell research, International Journal of Public Opinion Research, 17 (2005), 90-112.
doi: 10.1093/ijpor/edh058. |
[12] |
H. Norpohth, M. S. L. Beck and J. D. Lafay, Economics and Politics: The Calculus of Support, University of Michigan Press, 1991. |
[13] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[14] |
R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49 (2004), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[15] |
A. Sarlette, Geometry and Symmetries in Coordination Control, PhD thesis, Université de Liège, 2009. |
[16] |
A. Sarlette and R. Sepulchre, Consensus optimization on manifolds, SIAM Journal on Control and Optimization, 48 (2009), 56-76.
doi: 10.1137/060673400. |
[17] |
D. A. Scheufele and B. V. Lewenstein, The public and nanotechnology: How citizens make sense of emerging technologies, Journal of Nanoparticle Research, 7 (2005), 659-667.
doi: 10.1007/s11051-005-7526-2. |
[18] |
R. Sepulchre, Consensus on nonlinear spaces, Annual reviews in control, 35 (2011), 56-64.
doi: 10.1016/j.arcontrol.2011.03.003. |
[19] |
P. Sobkowicz, Modelling opinion formation with physics tools: Call for closer link with reality, Journal of Artificial Societies and Social Simulation, 12 (2009), 11pp, URL http://jasss.soc.surrey.ac.uk/12/1/11.html. |
[20] |
S. H. Strogatz, From kuramoto to crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, 143 (2000), 1-20, URL http://www.sciencedirect.com/science/article/pii/S0167278900000944.
doi: 10.1016/S0167-2789(00)00094-4. |
[21] |
K. Sznajd-Weron and J. Sznajd, Opinion evolution in closed community, International Journal of Modern Physics C, 11 (2000), 1157-1165.
doi: 10.1142/S0129183100000936. |
[22] |
J. N. Tsitsiklis, Problems in Decentralized Decision making and Computation., PhD thesis, MIT, 1984. |
[23] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Physical review letters, 75 (1995), p1226.
doi: 10.1103/PhysRevLett.75.1226. |
show all references
References:
[1] |
L. Behera and F. Schweitzer, On spatial consensus formation: Is the sznajd model different from a voter model?, International Journal of Modern Physics C, 14 (2003), 1331-1354.
doi: 10.1142/S0129183103005467. |
[2] |
V. D. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, 48 (2010), 5214-5240.
doi: 10.1137/090766188. |
[3] |
G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Advances in Complex Systems, 3 (2000), 87-98.
doi: 10.1142/S0219525900000078. |
[4] |
R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence models, analysis, and simulation,, Journal of Artificial Societies and Social Simulation, 5 ().
|
[5] |
J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national academy of sciences, 79 (1982), 2554-2558.
doi: 10.1073/pnas.79.8.2554. |
[6] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, Automatic Control, IEEE Transactions on, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[7] |
Y. Kuramoto, Cooperative dynamics of oscillator community a study based on lattice of rings, Progress of Theoretical Physics Supplement, 79 (1984), 223-240.
doi: 10.1143/PTPS.79.223. |
[8] |
J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, International Journal of Modern Physics C, 18 (2007), 1819-1838.
doi: 10.1142/S0129183107011789. |
[9] |
L. Moreau, Stability of continuous-time distributed consensus algorithms, in Decision and Control, 2004. CDC. 43rd IEEE Conference on, vol. 4, IEEE, (2004), 3998-4003.
doi: 10.1109/CDC.2004.1429377. |
[10] |
L. Moreau, Stability of multiagent systems with time-dependent communication links, Automatic Control, IEEE Transactions on, 50 (2005), 169-182.
doi: 10.1109/TAC.2004.841888. |
[11] |
M. C. Nisbet, The competition for worldviews: Values, information, and public support for stem cell research, International Journal of Public Opinion Research, 17 (2005), 90-112.
doi: 10.1093/ijpor/edh058. |
[12] |
H. Norpohth, M. S. L. Beck and J. D. Lafay, Economics and Politics: The Calculus of Support, University of Michigan Press, 1991. |
[13] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[14] |
R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49 (2004), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[15] |
A. Sarlette, Geometry and Symmetries in Coordination Control, PhD thesis, Université de Liège, 2009. |
[16] |
A. Sarlette and R. Sepulchre, Consensus optimization on manifolds, SIAM Journal on Control and Optimization, 48 (2009), 56-76.
doi: 10.1137/060673400. |
[17] |
D. A. Scheufele and B. V. Lewenstein, The public and nanotechnology: How citizens make sense of emerging technologies, Journal of Nanoparticle Research, 7 (2005), 659-667.
doi: 10.1007/s11051-005-7526-2. |
[18] |
R. Sepulchre, Consensus on nonlinear spaces, Annual reviews in control, 35 (2011), 56-64.
doi: 10.1016/j.arcontrol.2011.03.003. |
[19] |
P. Sobkowicz, Modelling opinion formation with physics tools: Call for closer link with reality, Journal of Artificial Societies and Social Simulation, 12 (2009), 11pp, URL http://jasss.soc.surrey.ac.uk/12/1/11.html. |
[20] |
S. H. Strogatz, From kuramoto to crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, 143 (2000), 1-20, URL http://www.sciencedirect.com/science/article/pii/S0167278900000944.
doi: 10.1016/S0167-2789(00)00094-4. |
[21] |
K. Sznajd-Weron and J. Sznajd, Opinion evolution in closed community, International Journal of Modern Physics C, 11 (2000), 1157-1165.
doi: 10.1142/S0129183100000936. |
[22] |
J. N. Tsitsiklis, Problems in Decentralized Decision making and Computation., PhD thesis, MIT, 1984. |
[23] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Physical review letters, 75 (1995), p1226.
doi: 10.1103/PhysRevLett.75.1226. |
[1] |
Simone Fagioli, Emanuela Radici. Opinion formation systems via deterministic particles approximation. Kinetic and Related Models, 2021, 14 (1) : 45-76. doi: 10.3934/krm.2020048 |
[2] |
Marina Dolfin, Mirosław Lachowicz. Modeling opinion dynamics: How the network enhances consensus. Networks and Heterogeneous Media, 2015, 10 (4) : 877-896. doi: 10.3934/nhm.2015.10.877 |
[3] |
Laura Gardini, Iryna Sushko. Preface: Special issue on nonlinear dynamical systems in economic modeling. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : i-iv. doi: 10.3934/dcdsb.2021241 |
[4] |
Daniel Lear, David N. Reynolds, Roman Shvydkoy. Grassmannian reduction of cucker-smale systems and dynamical opinion games. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5765-5787. doi: 10.3934/dcds.2021095 |
[5] |
Sergei Yu. Pilyugin, M. C. Campi. Opinion formation in voting processes under bounded confidence. Networks and Heterogeneous Media, 2019, 14 (3) : 617-632. doi: 10.3934/nhm.2019024 |
[6] |
Pierre Degond, Gadi Fibich, Benedetto Piccoli, Eitan Tadmor. Special issue on modeling and control in social dynamics. Networks and Heterogeneous Media, 2015, 10 (3) : i-ii. doi: 10.3934/nhm.2015.10.3i |
[7] |
Masatoshi Shiino, Keiji Okumura. Control of attractors in nonlinear dynamical systems using external noise: Effects of noise on synchronization phenomena. Conference Publications, 2013, 2013 (special) : 685-694. doi: 10.3934/proc.2013.2013.685 |
[8] |
Aylin Aydoğdu, Sean T. McQuade, Nastassia Pouradier Duteil. Opinion Dynamics on a General Compact Riemannian Manifold. Networks and Heterogeneous Media, 2017, 12 (3) : 489-523. doi: 10.3934/nhm.2017021 |
[9] |
Robin Cohen, Alan Tsang, Krishna Vaidyanathan, Haotian Zhang. Analyzing opinion dynamics in online social networks. Big Data & Information Analytics, 2016, 1 (4) : 279-298. doi: 10.3934/bdia.2016011 |
[10] |
Aleksandar Zatezalo, Dušan M. Stipanović. Control of dynamical systems with discrete and uncertain observations. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4665-4681. doi: 10.3934/dcds.2015.35.4665 |
[11] |
Elena Goncharova, Maxim Staritsyn. Optimal control of dynamical systems with polynomial impulses. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4367-4384. doi: 10.3934/dcds.2015.35.4367 |
[12] |
Tayel Dabbous. Adaptive control of nonlinear systems using fuzzy systems. Journal of Industrial and Management Optimization, 2010, 6 (4) : 861-880. doi: 10.3934/jimo.2010.6.861 |
[13] |
David L. Russell. Modeling and control of hybrid beam systems with rotating tip component. Evolution Equations and Control Theory, 2014, 3 (2) : 305-329. doi: 10.3934/eect.2014.3.305 |
[14] |
Silviu-Iulian Niculescu, Peter S. Kim, Keqin Gu, Peter P. Lee, Doron Levy. Stability crossing boundaries of delay systems modeling immune dynamics in leukemia. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 129-156. doi: 10.3934/dcdsb.2010.13.129 |
[15] |
Doron Levy, Tiago Requeijo. Modeling group dynamics of phototaxis: From particle systems to PDEs. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 103-128. doi: 10.3934/dcdsb.2008.9.103 |
[16] |
Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic and Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001 |
[17] |
Domenica Borra, Tommaso Lorenzi. Asymptotic analysis of continuous opinion dynamics models under bounded confidence. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1487-1499. doi: 10.3934/cpaa.2013.12.1487 |
[18] |
Clinton Innes, Razvan C. Fetecau, Ralf W. Wittenberg. Modelling heterogeneity and an open-mindedness social norm in opinion dynamics. Networks and Heterogeneous Media, 2017, 12 (1) : 59-92. doi: 10.3934/nhm.2017003 |
[19] |
Francesco Fassò, Simone Passarella, Marta Zoppello. Control of locomotion systems and dynamics in relative periodic orbits. Journal of Geometric Mechanics, 2020, 12 (3) : 395-420. doi: 10.3934/jgm.2020022 |
[20] |
Urszula Ledzewicz, Heinz Schättler. Pitfalls in applying optimal control to dynamical systems: An overview and editorial perspective. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022016 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]