Nonlinear Opinion Dynamics With Tunable Sensitivity

Agreement; bifurcation; bio-inspired engineering; deadlock breaking; decision making; disagreement; multi-agent systems; network centrality; networked control systems; nonlinear dynamical systems; opinion dynamics; Adaptation models; Biological system modeling; Continous time; Dynamic scheduling; Generalisation; Linear weighted averages; Opinion dynamics; Robustness; Sensitivity; Tunables; Control and Systems Engineering; Computer Science Applications; Electrical and Electronic Engineering

Abstract :

[en] We propose a continuous-time multioption nonlinear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models. For a group of agents that communicate opinions over a network, these behaviors include multistable agreement and disagreement, tunable sensitivity to input, robustness to disturbance, flexible transition between patterns of opinions, and opinion cascades. We derive network-dependent tuning rules to robustly control the system behavior and we design state-feedback dynamics for the model parameters to make the behavior adaptive to changing external conditions. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision-making and dynamic task allocation.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Bizyaeva, Anastasia ; Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, United States

Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; National Autonomous University of Mexico, Mathematics Department, CDMX, Mexico

Leonard, Naomi Ehrich ; Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, United States

Language :

English

Title :

Nonlinear Opinion Dynamics With Tunable Sensitivity

Publication date :

March 2023

Journal title :

IEEE Transactions on Automatic Control

ISSN :

0018-9286

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Issue :

Pages :

1415 - 1430

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://ieeexplore.ieee.org/ielam/9/10056266/9736598-aam.pdf

Funders :

NSF - National Science Foundation
ONR - Office of Naval Research
UNAM - Universidad Nacional Autónoma de México
CONACYT - Consejo Nacional de Ciencia y Tecnología

Funding text :

DGAPA-UNAM PAPIIT; Graduate Research Fellowship

Available on ORBi :

since 27 May 2023

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Bibliography

M. H. DeGroot, "Reaching a consensus," J. Amer. Stat. Assoc., vol. 69, no. 345, pp. 121-132, 1974.
N. E. Friedkin and E. C. Johnsen, "Social influence networks and opinion change," in Advances in Group Processes, vol. 16. Bingley, U.K.: Emerald Group Publishing Limited, 1999, pp. 1-29.
P. Cisneros-Velarde, K. S. Chan, and F. Bullo, "Polarization and fluctuations in signed social networks," IEEE Trans. Autom. Control, vol. 66, no. 8, pp. 3789-3793, Aug. 2021.
R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
C. Altafini, "Consensus problems on networks with antagonistic interactions," IEEE Trans. Autom.Control, vol. 58, no. 4, pp. 935-946, Apr. 2013.
G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, "Mixing beliefs among interacting agents," Adv. Complex Syst., vol. 3, no. 1-4, pp. 87-98, 2000.
R. Hegselmann and U. Krause, "Opinion dynamics and bounded confidence models, analysis, and simulations," J. Artif. Societies Social Simul., vol. 5, no. 3, pp. 121-132, 2002.
R.Hegselmann and U. Krause, "Opinion dynamics driven by variousways of averaging," Comput. Econ., vol. 25, no. 4, pp. 381-405, 2005.
V. Blondel, J. M. Hendrickx, and J.N. Tsitsiklis, "On Krause's multi-agent consensus model with state-dependent connectivity," IEEE Trans. Autom. Control, vol. 54, no. 11, pp. 2586-2597, Nov. 2009.
P. Dandekar, A. Goel, and D. T. Lee, "Biased assimilation, homophily, and the dynamics of polarization," Proc. Nat. Acad. Sci. USA, vol. 110, no. 15, pp. 5791-5796, 2013.
W. Xia, M. Ye, J. Liu, M. Cao, and X.-M. Sun, "Analysis of a nonlinear opinion dynamics model with biased assimilation," Automatica, vol. 120, 2020, Art. no. 109113.
P. Jia, A. MirTabatabaei, N. E. Friedkin, and F. Bullo, "Opinion dynamics and the evolution of social power in influence networks," SIAM Rev., vol. 57, no. 3, pp. 367-397, 2015.
M. Ye, J. Liu, B. D. O. Anderson, C. Yu, and T. Basar, "Evolution of social power in social networks with dynamic topology," IEEE Trans. Aut. Control, vol. 63, no. 11, pp. 3793-3808, Nov. 2018.
A. Franci, V. Srivastava, and N. E. Leonard, "A realization theory for bio-inspired collective decision making," Nov. 2017, arXiv:1503.08526.
A. Fontan and C.Altafini, "Multiequilibria analysis for a class of collective decision-making networked systems," IEEE Trans. Control Netw. Syst., vol. 5, no. 4, pp. 1931-1940, Dec. 2018.
R. Gray,A. Franci,V. Srivastava, and N. E. Leonard, "Multiagent decisionmaking dynamics inspired by honeybees," IEEE Trans. Control Netw. Syst., vol. 5, no. 2, pp. 793-806, Jun. 2018.
P. U. Abara, F. Ticozzi, and C. Altafini, "Spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems," IEEE Trans. Autom. Control, vol. 63, no. 2, pp. 402-417, Feb. 2018.
A. Fontan and C. Altafini, "Achieving a decision in antagonistic multi agent networks: Frustration determines commitment strength," in Proc. IEEE Conf. Decis. Control, 2018, pp. 109-114.
L. Ding,W. X. Zheng, andG.Guo, "Network-based practical set consensus of multi-agent systems subject to input saturation," Automatica, vol. 89, pp. 316-324, 2018.
A. Hu, J. Cao, M. Hu, and L. Guo, "Event-triggered group consensus for multi-agent systems subject to input saturation," J. Franklin Inst., vol. 355, no. 15, pp. 7384-7400, 2018.
R. E. Mirollo and S. H. Strogatz, "Jump bifurcation and hysteresis in an infinite-dimensional dynamical system of coupled spins," SIAM J. Appl. Math., vol. 50, no. 1, pp. 108-124, 1990.
B. Nabet, N. E. Leonard, I. D. Couzin, and S. A. Levin, "Dynamics of decision making in animal group motion," J. Nonlinear Sci., vol. 19, pp. 399-435, 2009.
N. E. Leonard, T. Shen, B. Nabet, L. Scardovi, I. D. Couzin, and S. A. Levin, "Decision versus compromise for animal groups in motion," Proc. Nat. Acad. Sci. USA, vol. 109, no. 1, pp. 227-232, 2012.
D. Pais, P. M. Hogan, T. Schlegel, N. R. Franks, and N. E. Leonard, "A mechanism for value-sensitive decision-making," PLoS One, vol. 8, pp. 1-9, 2013.
I. Pinkoviezky, I. D. Couzin, and N. Gov, "Collective conflict resolution in groups on the move," Phys. Rev. E, vol. 97, 2018, Art. no. 032304.
A. F. Siegenfeld and Y. Bar-Yam, "Negative representation and instability in democratic elections," Nature Phys., vol. 16, pp. 186-190, 2020.
W. Mei, F. Bullo, G. Chen, J. M. Hendrickx, and F. Dörfler, "Rethinking the micro-foundation of opinion dynamics: Rich consequences of an inconspicuous change," IFAC-PapersOnLine, vol. 53, no. 5, pp. 307-310, 2020.
J. Liu, X. Chen, T. Basar, and M. A. Belabbas, "Exponential convergence of the discrete-and continuous-time Altafini models," IEEE Trans. Autom. Control, vol. 62, no. 12, pp. 6168-6182, Dec. 2017.
G. Shi, C. Altafini, and J. S. Baras, "Dynamics over signed networks," SIAM Rev., vol. 61, no. 2, pp. 229-257, 2019.
A. Franci, M. Golubitsky, A. Bizyaeva, and N. E. Leonard, "A modelindependent theory of consensus and dissensus decision making," Sep. 2020, arXiv:1909.05765.
H. R. Wilson and J. D. Cowan, "Excitatory and inhibitory interactions in localized populations of model neurons," Biophysical J., vol. 12, no. 1, pp. 1-24, 1972.
H. R. Wilson and J. D. Cowan, "A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue," Kybernetik, vol. 13, no. 2, pp. 55-80, 1973.
J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Nat. Acad. Sci. USA, vol. 79, no. 8, pp. 2554-2558, 1982.
J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci. USA, vol. 81, no. 10, pp. 3088-3092, 1984.
Y. Nakamura, K. Torii, and T. Munakata, "Neural-network model composed of multidimensional spin neurons," Phys. Rev. E, vol. 51, no. 2, pp. 1538-1546, 1995.
M. Usher and J. L. McClelland, "The time course of perceptual choice: The leaky, competing accumulator model," Psychol. Rev., vol. 108, no. 3, pp. 550-592, 2001.
R. Bogacz and K. Gurney, "The basal ganglia and cortex implement optimal decision making between alternative actions," Neural Computation, vol. 19, no. 2, pp. 442-477, 2007.
D. Liu and A. N. Michel, Dynamical Systems With Saturation Nonlinearities: Analysis and Design. Berlin, Germany: Springer-Verlag, 1994.
T. Hu and Z. Lin, Control SystemsWith Actuator Saturation: Analysis and Design. Berlin, Germany: Springer, 2001.
S. Fortunato, V. Latora, A. Pluchino, and A. Rapisarda, "Vector opinion dynamics in a bounded confidence consensusmodel," Int. J. Modern Phys. C, vol. 16, p. 1535-1551, 2005.
A. Nedić and B. Touri, "Multi-dimensional Hegselmann-Krause dynamics," in Proc. IEEE Conf. Decis. Control, 2012, pp. 68-73.
L. Li, A. Scaglione, A. Swami, and Q. Zhao, "Consensus, polarization and clustering of opinions in social networks," IEEE J. Sel. Areas Commun., vol. 31, no. 6, pp. 1072-1083, Jun. 2013.
N. E. Friedkin, A. V. Proskurnikov, R. Tempo, and S. E. Parsegov, "Network science on belief system dynamics under logic constraints," Science, vol. 354, no. 6310, pp. 321-326, 2016.
S. E. Parsegov, A. V. Proskurnikov, R. Tempo, and N. E. Friedkin, "Novel multidimensional models of opinion dynamics in social networks," IEEE Trans. Autom. Control, vol. 62, no. 5, pp. 2270-2285, May 2017.
L. Pan, H. Shao, M. Mesbahi, Y. Xi, and D. Li, "Bipartite consensus on matrix-valued weighted networks," IEEE Trans. Circuits Syst. II: Exp. Briefs, vol. 66, no. 8, pp. 1441-1445, Aug. 2019.
M. Ye, J. Liu, L. Wang, B. D. O. Anderson, and M. Cao, "Consensus and disagreement of heterogeneous belief systems in influence networks," IEEE Trans. Autom. Control, vol. 65, no. 11, pp. 4679-4694, Nov. 2020.
S. Park, A. Bizyaeva, M. Kawakatsu, A. Franci, and N. Leonard, "Tuning cooperative behavior in games with nonlinear opinion dynamics," IEEE Control Syst. Lett., vol. 6, pp. 2030-2035, 2022.
J. Ghaderi and R. Srikant, "Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate," Automatica, vol. 50, pp. 3209-3215, 2014.
A. Franci, A. Bizyaeva, S. Park, and N. E. Leonard, "Analysis and control of agreement and disagreement opinion cascades," Swarm Intell., vol. 15, pp. 47-82, 2021.
M. Golubitsky and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Ser. Applied Mathematical Sciences, vol. 51. New York, NY, USA: Springer-Verlag, 1985.
A. Fontan and C. Altafini, "The role of frustration in collective decisionmaking dynamical processes onmultiagent signed networks," IEEE Trans. Autom. Control, to be published, doi: 10.1109/TAC.2021.3123222.
D. Meng, M. Du, and Y. Jia, "Interval bipartite consensus of networked agents associated with signed digraphs," IEEE Trans. Autom. Control, vol. 61, no. 12, pp. 3755-3770, Dec. 2016.
A. V. Proskurnikov, A. S. Matveev, and M. Cao, "Opinion dynamics in social networks with hostile camps: Consensus vs. polarization," IEEE Trans. Autom. Control, vol. 61, no. 6, pp. 1524-1536, Jun. 2016.
S. Musslick, A. Bizyaeva, S. Agaron, N. E. Leonard, and J. D. Cohen, "Stability-flexibility dilemma in cognitive control: A dynamical system perspective," in Proc. Annu. Meeting Cogn. Sci. Soc., Montreal, Canada, 2019, pp. 1-7.
N. E. Leonard, K. Lipsitz, A. Bizyaeva, A. Franci, and Y. Lelkes, "The nonlinear feedback dynamics of asymmetric political polarization," Proc. Nat. Acad. Sci. USA, vol. 118, no. 50, 2021, Art. no. e2102149118.
A. Pogromsky, G. Santoboni, and H. Nijmeijer, "Partial synchronization: From symmetry towards stability," Physica D: Nonlinear Phenomena, vol. 172, no. 1-4, pp. 65-87, 2002.
W. Xia and M. Cao, "Clustering in diffusively coupled networks," Automatica, vol. 47, no. 11, pp. 2395-2405, 2011.
I. Stewart, M. Golubitsky, and M. Pivato, "Symmetry groupoids and patterns of synchrony in coupled cell networks," SIAM J. Appl. Dynamical Syst., vol. 2, no. 4, pp. 609-646, 2003.
N. O'Clery, Y. Yuan, G.-B. Stan, and M. Barahona, "Observability and coarse graining of consensus dynamics through the external equitable partition," Phys. Rev. E, vol. 88, no. 4, 2013, Art. no. 042805.
M. T. Schaub, N. O'Clery, Y. N. Billeh, J.-C. Delvenne, R. Lambiotte, and M. Barahona, "Graph partitions and cluster synchronization in networks of oscillators," Chaos An Interdiscipl. J. Nonlinear Sci., vol. 26, no. 9, 2016, Art. no. 094821.
F. Sorrentino, L. M. Pecora, A.M. Hagerstrom, T. E. Murphy, and R. Roy, "Complete characterization of the stability of cluster synchronization in complex dynamical networks," Sci. Adv., vol. 2, no. 4, Art. no. e1501737, 2016.
L. V. Gambuzza and M. Frasca, "A criterion for stability of cluster synchronization in networks with external equitable partitions," Automatica, vol. 100, pp. 212-218, 2019.
M. Golubitsky and I. Stewart, The Symmetry Perspective, 1st ed., Ser. Progress in Mathematics, vol. 200. Basel, Switzerland: Birkhäuser Basel, 2002.
A. Bizyaeva, A. Matthews, A. Franci, and N. E. Leonard, "Patterns of nonlinear opinion formation on networks," in Proc. Amer. Control Conf., 2021, pp. 2739-2744.
A. Reina, J. A. R. Marshall, V. Trianni, and T. Bose, "Model of the best-of-N nest-site selection process in honeybees," Phys. Rev. E, vol. 95, 2017, Art. no. 052411.
K. Wang and N. Michel, "Robustness and perturbation analysis of a class of nonlinear systems with applications to neural networks," IEEE Trans. Circuits Syst. I, vol. 41, no. 1, pp. 24-32, Jan. 1994.
A. Bizyaeva, T. Sorochkin, A. Franci, and N. E. Leonard, "Control of agreement and disagreement cascades with distributed inputs," in Proc. IEEE Conf. Decis. Control, 2021, pp. 4994-4999.
A. Dhooge, W. Govaerts, Y. Kuznetsov, H. Meijer, and B. Sautois, "New features of the software MatCont for bifurcation analysis of dynamical systems," Math. Comput. Model. Dyn. Syst., vol. 14, no. 2, pp. 147-175, 2008.
R. Sepulchre, D. A. Paley, and N. E. Leonard, "Stabilization of planar collective motion with limited communication," IEEE Trans. Autom. Control, vol. 53, no. 3, pp. 706-719, Apr. 2008.
S. H. Strogatz, "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Physica D: Nonlinear Phenomena, vol. 143, no. 1-4, pp. 1-20, 2000.
M. H. et al., "Python-ternary: Ternary plots in Python," Zenodo, doi: 10.5281/zenodo.594435. [Online]. Available: https://github.com/mar charper/python-ternary
M. Golubitsky, I. Stewart, and D. Shaeffer, Singularities and Groups in Bifurcation Theory, vol. II, ser. Applied Mathematical Sciences, vol. 69. Berlin, Germany: Springer-Verlag, 1988.
Y. D. Zhong and N. E. Leonard, "A continuous threshold model of cascade dynamics," in Proc. IEEE Conf. Decis. Control, 2019, pp. 1704-1709.
H. Khalil, Nonlinear Systems, 3rd ed. New York City, NY, USA: Pearson Education, 2000.
J. Lorenz, "Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus," Eur. J. Econ. Soc. Syst., vol. 19, pp. 213-227, 2006.
A. Sirbu, V. Loreto, V. D. P. Servedio, and F. Tria, "Opinion dynamics with disagreement and modulated information," J. Stat. Phys., vol. 151, no. 1, pp. 218-237, 2013.