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On a discrete threedimensional LeslieGower competition model
The hipster effect: When anticonformists all look the same
Department of Mathematics and Volen National Center for Complex Systems, Brandeis University, 415 South Street, Waltham, MA 02453, USA 
In such different domains as statistical physics, neurosciences, spin glasses, social science, economics and finance, large ensemble of interacting individuals evolving following (mainstream) or against (hipsters) the majority are ubiquitous. Moreover, in a variety of applications, interactions between agents occur after specific delays that depends on the time needed to transport, transmit or take into account information. This paper focuses on the role of opposition to majority and delays in the emerging dynamics in a population composed of mainstream and anticonformist individuals. To this purpose, we introduce a class of simple statistical system of interacting agents taking into account (ⅰ) the presence of mainstream and anticonformist individuals and (ⅱ) delays, possibly heterogeneous, in the transmission of information. In this simple model, each agent can be in one of two states, and can change state in continuous time with a rate depending on the state of others in the past. We express the thermodynamic limit of these systems as the number of agents diverge, and investigate the solutions of the limit equation, with a particular focus on synchronized oscillations induced by delayed interactions. We show that when hipsters are too slow in detecting the trends, they will consistently make the same choice, and realizing this too late, they will switch, all together to another state where they remain alike. Another modality synchronizing hipsters are asymmetric interactions, particularly when the crossinteraction between hipsters and mainstreams aree prominent, i.e. when hipsters radically oppose to mainstream and mainstreams wish to follow the majority, even when led by hipsters. We demonstrate this phenomenon analytically using bifurcation theory and reduction to normal form. We find that, in the case of asymmetric interactions, the level of randomness in the decisions themselves also leads to synchronization of the hipsters. Beyond the choice of the best suit to wear this winter, this study may have important implications in understanding synchronization of nerve cells, investment strategies in finance, or emergent dynamics in social science, domains in which delays of communication and the geometry of information accessibility are prominent.
References:
[1] 
L. Boltzmann, Lectures on Gas Theory, Translated by Stephen G. Brush University of California Press, BerkeleyLos Angeles, Calif. 1964. Google Scholar 
[2] 
N. Brunel and V. Hakim, Fast global oscillations in networks of integrateandfire neurons with low firing rates, Neural Computation, 11 (1999), 16211671. doi: 10.1162/089976699300016179. Google Scholar 
[3] 
J. Carr, Applications of Centre Manifold Theory, SpringerVerlag, 1981. Google Scholar 
[4] 
D. Challet, M. Marsili and Y.Ch. Zhang, Modeling market mechanism with minority game, Physica A: Statistical Mechanics and its Applications, 276 (2000), 284315. doi: 10.1016/S03784371(99)00446X. Google Scholar 
[5] 
D. Challet, M. Marsili and Y.Ch. Zhang, Minority Games: Interacting Agents in Financial Markets, OUP Catalogue, 2013. Google Scholar 
[6] 
A. Clauset, C. R. Shalizi and M. E. J. Newman, Powerlaw distributions in empirical data, SIAM review, 51 (2009), 661703. doi: 10.1137/070710111. Google Scholar 
[7] 
F. Collet, M. Formentin and D. Tovazzi, Rhythmic behavior in a twopopulation meanfield ising model, Physical Review E, 94 (2016), 042139, 7pp. doi: 10.1103/PhysRevE.94.042139. Google Scholar 
[8] 
A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model, Physical Review A, 36 (1987), 49224939. doi: 10.1103/PhysRevA.36.4922. Google Scholar 
[9] 
A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bounds: Ising spins and glauber dynamics, Phys. Review A, 37 (1987), 48654874. doi: 10.1103/PhysRevA.37.4865. Google Scholar 
[10] 
P. Dai Pra, M. Fischer and D. Regoli, A curieweiss model with dissipation, Journal of Statistical Physics, 152 (2013), 3753. doi: 10.1007/s1095501307562. Google Scholar 
[11] 
P. Dai Pra, E. Sartori and M. Tolotti, Rhytmic behavior in large scale systems: a model related to meanfield games, preprint, http://www.math.unipd.it/ daipra/draftGamePaolo.pdf, 2017.Google Scholar 
[12] 
P. D. Pra, E. Sartori and M. Tolotti, Climb on the bandwagon: Consensus and periodicity in a lifetime utility model with strategic interactions, arXiv: 1804.07469, 2018.Google Scholar 
[13] 
A. Dhooge, W. Govaerts, Y. A. Kuznetsov, W. Mestrom, A. M. Riet and B. Sautois, Matcont and cl Matcont: Continuation Toolboxes in Matlab, Universiteit Gent, Belgium and Utrecht University, The Netherlands, 2006.Google Scholar 
[14] 
A. Dhooge, W. Govaerts and Y. A. Kuznetsov, Matcont: A matlab package for numerical bifurcation analysis of odes, ACM Transactions on Mathematical Software (TOMS), 29 (2003), 141164. doi: 10.1145/779359.779362. Google Scholar 
[15] 
B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, volume 14., Siam, 2002. doi: 10.1137/1.9780898718195. Google Scholar 
[16] 
T. Faria, On a planar system modelling a neuro network with memory, Journal of Differential Equations, 168 (2000), 129149. doi: 10.1006/jdeq.2000.3881. Google Scholar 
[17] 
S. Galam, Sociophysics: A Physicist's Modeling of PsychoPolitical Phenomena, Springer, 2012. doi: 10.1007/9781461420323. Google Scholar 
[18] 
F. Giannakopoulos and A. Zapp, Local and global hopf bifurcation in a scalar delay differential equation, Journal of Mathematical Analysis and Applications, 237 (1999), 425450. doi: 10.1006/jmaa.1999.6431. Google Scholar 
[19] 
J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, volume 42 of Applied mathematical sciences, Springer, 1983. doi: 10.1007/9781461211402. Google Scholar 
[20] 
J. Haidt, Disagreeing virtuously, Disagreeing Virtuously, page 138, 2017.Google Scholar 
[21] 
J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer Verlag, 1993. doi: 10.1007/9781461243427. Google Scholar 
[22] 
G. Hermann and J. Touboul, Heterogeneous connections induce oscillations in largescale networks, Physical Review Letters, 109 (2012), 018702. doi: 10.1103/PhysRevLett.109.018702. Google Scholar 
[23] 
A. Jackson and D. Ladley, Market ecologies: The effect of information on the interaction and profitability of technical trading strategies, International Review of Financial Analysis, 47 (2016), 270280. doi: 10.1016/j.irfa.2016.02.007. Google Scholar 
[24] 
J. S. Juul and M. A. Porter, Hipsters on networks: How a small group of individuals can lead to an antiestablishment majority, arXiv: 1707.07187, 2017.Google Scholar 
[25] 
Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, volume 112., SpringerVerlag, New York, 1995. doi: 10.1007/9781475724219. Google Scholar 
[26] 
J. Plevin, Who's a Hipster, The Huffington Post, 2008.Google Scholar 
[27] 
C. Quiñinao and J. Touboul, Limits and dynamics of randomly connected neuronal networks, Acta Applicandae Mathematicae, 136 (2015), 167192. doi: 10.1007/s1044001499455. Google Scholar 
[28] 
A. Roxin, N. Brunel and D. Hansel, Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks, Physical Review Letters, 94 (2005), 238103. doi: 10.1103/PhysRevLett.94.238103. Google Scholar 
[29] 
M. Scheutzow, Noise can create periodic behavior and stabilize nonlinear diffusions, Stochastic Processes and Their Applications, 20 (1985), 323331. doi: 10.1016/03044149(85)902194. Google Scholar 
[30] 
M. Scheutzow, Some examples of nonlinear diffusion processes having a timeperiodic law, The Annals of Probability, 13 (1985), 379384. doi: 10.1214/aop/1176992997. Google Scholar 
[31] 
D. Sherrington and S. Kirkpatrick, Solvable model of a spinglass, Spin Glass Theory and Beyond, 35 (1986), 104108. doi: 10.1142/9789812799371_0010. Google Scholar 
[32] 
H. Sompolinsky, A. Crisanti and H.J. Sommers, Chaos in random neural networks, Physical Review Letters, 61 (1988), 259262. doi: 10.1103/PhysRevLett.61.259. Google Scholar 
[33]  S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second edition, Westview Press, Boulder, CO, 2015. Google Scholar 
[34] 
A.S. Sznitman, Topics in propagation of chaos, In Ecole d'Eté de Probabilités de SaintFlour XIX, 165–251, Lecture Notes in Math., 1464, Springer, Berlin, 1991. doi: 10.1007/BFb0085169. Google Scholar 
[35] 
J. Touboul, Limits and dynamics of stochastic neuronal networks with random heterogeneous delays, Journal of Statistical Physics, 149 (2012), 569597. doi: 10.1007/s1095501206076. Google Scholar 
[36] 
J. Touboul, The hipster effect: When anticonformists all look the same, arXiv: 1410.8001, 2014.Google Scholar 
[37] 
J. Touboul, G. Hermann and O. Faugeras, Noiseinduced behaviors in neural mean field dynamics, SIAM Journal on Applied Dynamical Systems, 11 (2012), 4981. doi: 10.1137/110832392. Google Scholar 
show all references
References:
[1] 
L. Boltzmann, Lectures on Gas Theory, Translated by Stephen G. Brush University of California Press, BerkeleyLos Angeles, Calif. 1964. Google Scholar 
[2] 
N. Brunel and V. Hakim, Fast global oscillations in networks of integrateandfire neurons with low firing rates, Neural Computation, 11 (1999), 16211671. doi: 10.1162/089976699300016179. Google Scholar 
[3] 
J. Carr, Applications of Centre Manifold Theory, SpringerVerlag, 1981. Google Scholar 
[4] 
D. Challet, M. Marsili and Y.Ch. Zhang, Modeling market mechanism with minority game, Physica A: Statistical Mechanics and its Applications, 276 (2000), 284315. doi: 10.1016/S03784371(99)00446X. Google Scholar 
[5] 
D. Challet, M. Marsili and Y.Ch. Zhang, Minority Games: Interacting Agents in Financial Markets, OUP Catalogue, 2013. Google Scholar 
[6] 
A. Clauset, C. R. Shalizi and M. E. J. Newman, Powerlaw distributions in empirical data, SIAM review, 51 (2009), 661703. doi: 10.1137/070710111. Google Scholar 
[7] 
F. Collet, M. Formentin and D. Tovazzi, Rhythmic behavior in a twopopulation meanfield ising model, Physical Review E, 94 (2016), 042139, 7pp. doi: 10.1103/PhysRevE.94.042139. Google Scholar 
[8] 
A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model, Physical Review A, 36 (1987), 49224939. doi: 10.1103/PhysRevA.36.4922. Google Scholar 
[9] 
A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bounds: Ising spins and glauber dynamics, Phys. Review A, 37 (1987), 48654874. doi: 10.1103/PhysRevA.37.4865. Google Scholar 
[10] 
P. Dai Pra, M. Fischer and D. Regoli, A curieweiss model with dissipation, Journal of Statistical Physics, 152 (2013), 3753. doi: 10.1007/s1095501307562. Google Scholar 
[11] 
P. Dai Pra, E. Sartori and M. Tolotti, Rhytmic behavior in large scale systems: a model related to meanfield games, preprint, http://www.math.unipd.it/ daipra/draftGamePaolo.pdf, 2017.Google Scholar 
[12] 
P. D. Pra, E. Sartori and M. Tolotti, Climb on the bandwagon: Consensus and periodicity in a lifetime utility model with strategic interactions, arXiv: 1804.07469, 2018.Google Scholar 
[13] 
A. Dhooge, W. Govaerts, Y. A. Kuznetsov, W. Mestrom, A. M. Riet and B. Sautois, Matcont and cl Matcont: Continuation Toolboxes in Matlab, Universiteit Gent, Belgium and Utrecht University, The Netherlands, 2006.Google Scholar 
[14] 
A. Dhooge, W. Govaerts and Y. A. Kuznetsov, Matcont: A matlab package for numerical bifurcation analysis of odes, ACM Transactions on Mathematical Software (TOMS), 29 (2003), 141164. doi: 10.1145/779359.779362. Google Scholar 
[15] 
B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, volume 14., Siam, 2002. doi: 10.1137/1.9780898718195. Google Scholar 
[16] 
T. Faria, On a planar system modelling a neuro network with memory, Journal of Differential Equations, 168 (2000), 129149. doi: 10.1006/jdeq.2000.3881. Google Scholar 
[17] 
S. Galam, Sociophysics: A Physicist's Modeling of PsychoPolitical Phenomena, Springer, 2012. doi: 10.1007/9781461420323. Google Scholar 
[18] 
F. Giannakopoulos and A. Zapp, Local and global hopf bifurcation in a scalar delay differential equation, Journal of Mathematical Analysis and Applications, 237 (1999), 425450. doi: 10.1006/jmaa.1999.6431. Google Scholar 
[19] 
J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, volume 42 of Applied mathematical sciences, Springer, 1983. doi: 10.1007/9781461211402. Google Scholar 
[20] 
J. Haidt, Disagreeing virtuously, Disagreeing Virtuously, page 138, 2017.Google Scholar 
[21] 
J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer Verlag, 1993. doi: 10.1007/9781461243427. Google Scholar 
[22] 
G. Hermann and J. Touboul, Heterogeneous connections induce oscillations in largescale networks, Physical Review Letters, 109 (2012), 018702. doi: 10.1103/PhysRevLett.109.018702. Google Scholar 
[23] 
A. Jackson and D. Ladley, Market ecologies: The effect of information on the interaction and profitability of technical trading strategies, International Review of Financial Analysis, 47 (2016), 270280. doi: 10.1016/j.irfa.2016.02.007. Google Scholar 
[24] 
J. S. Juul and M. A. Porter, Hipsters on networks: How a small group of individuals can lead to an antiestablishment majority, arXiv: 1707.07187, 2017.Google Scholar 
[25] 
Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, volume 112., SpringerVerlag, New York, 1995. doi: 10.1007/9781475724219. Google Scholar 
[26] 
J. Plevin, Who's a Hipster, The Huffington Post, 2008.Google Scholar 
[27] 
C. Quiñinao and J. Touboul, Limits and dynamics of randomly connected neuronal networks, Acta Applicandae Mathematicae, 136 (2015), 167192. doi: 10.1007/s1044001499455. Google Scholar 
[28] 
A. Roxin, N. Brunel and D. Hansel, Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks, Physical Review Letters, 94 (2005), 238103. doi: 10.1103/PhysRevLett.94.238103. Google Scholar 
[29] 
M. Scheutzow, Noise can create periodic behavior and stabilize nonlinear diffusions, Stochastic Processes and Their Applications, 20 (1985), 323331. doi: 10.1016/03044149(85)902194. Google Scholar 
[30] 
M. Scheutzow, Some examples of nonlinear diffusion processes having a timeperiodic law, The Annals of Probability, 13 (1985), 379384. doi: 10.1214/aop/1176992997. Google Scholar 
[31] 
D. Sherrington and S. Kirkpatrick, Solvable model of a spinglass, Spin Glass Theory and Beyond, 35 (1986), 104108. doi: 10.1142/9789812799371_0010. Google Scholar 
[32] 
H. Sompolinsky, A. Crisanti and H.J. Sommers, Chaos in random neural networks, Physical Review Letters, 61 (1988), 259262. doi: 10.1103/PhysRevLett.61.259. Google Scholar 
[33]  S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second edition, Westview Press, Boulder, CO, 2015. Google Scholar 
[34] 
A.S. Sznitman, Topics in propagation of chaos, In Ecole d'Eté de Probabilités de SaintFlour XIX, 165–251, Lecture Notes in Math., 1464, Springer, Berlin, 1991. doi: 10.1007/BFb0085169. Google Scholar 
[35] 
J. Touboul, Limits and dynamics of stochastic neuronal networks with random heterogeneous delays, Journal of Statistical Physics, 149 (2012), 569597. doi: 10.1007/s1095501206076. Google Scholar 
[36] 
J. Touboul, The hipster effect: When anticonformists all look the same, arXiv: 1410.8001, 2014.Google Scholar 
[37] 
J. Touboul, G. Hermann and O. Faugeras, Noiseinduced behaviors in neural mean field dynamics, SIAM Journal on Applied Dynamical Systems, 11 (2012), 4981. doi: 10.1137/110832392. Google Scholar 
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