T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75 (6) (Aug 1995), 1226–1229.
 B. Birnir, An ODE model of the motion of pelagic fish, J. Stat. Phys. 128 (1/2) (2007), 535–568.Google Scholar
 A. Barbaro, B. Einarsson, B. Birnir, S. Sigurðsson, H. Valdimarsson, Ó.K. Pálsson, S. Sveinbjörnsson and Þ. Sigurðsson, Modelling and simulations of the migration of pelagic fish, ICES J. Mar. Sci. 66 (2009), 826–838.
 A. B. T. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents, Discrete and Continuous Dyn. Syst. Ser B 19 (2014), 1249–1278.Google Scholar
 S. H. Strogatz and R. E. Mirollo, Stability of incoherence in a population of coupled oscillators, J. Stat. Phys. 63 (3/4) (1991), 613–635.
 H. Chiba and I. Nishikawa, Center manifold reduction for large populations of globally coupled phase oscillators. Chaos 21 (2011), 043103. http://dx.doi.org/10.1063/1.3647317.Crossref
 A. B. T. Barbaro, K. Taylor, P. Trethewey, L. Youseff and B. Birnir, Discrete and continuous models of the behavior of pelagic fish: applications to the capelin, Math. Comput. Simul. 79 (12) (2009), 3397–3414.
 S. Hubbard, P. Babak, S. Sigurðsson and K. G. Magnússon, A model of the formation of fish schools and migration of fish, Ecol. Modell. 174 (2004), 359–374.Google Scholar
 Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, Lect. Notes Phys. 39 (1975), 420.Google Scholar
 A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Autom. Control 48 (6) (Jun 2003), 988–1001.Web of Science
 J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77 (2005), 137–185.Google Scholar
 R. E. Mirollo and S. H. Strogatz, The spectrum of the partially locked state for the Kuramoto model, J. Nonlinear Sci. 17 (2007), 309–347.Google Scholar
 H. Chiba, A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model, Ergodic Theory and Dyn. Syst. FirstView 8 (2014), 1–73.Google Scholar
 S. H. Strogatz, R. E. Mirollo and P. C. Matthews, Coupled nonlinear oscillators below the synchronization threshold: Relaxation be generalized Landau Damping. Phys. Rev. Lett. 68 (18) (1992), 2730–2733.
 P. E. Kloeden and E. Platen, Numerical solution of stochastic differential equations, Springer, Berlin, 1999.
 J. F. Cornejo, Effects of fish movement and environmental variability in the design and success of a marine protected area, PhD thesis, University of California, Santa Barbara, 2016.Google Scholar
 A. Huth and C. Wissel, The simulation of fish schools in comparison with experimental data, Ecol. Modell. 75 (1994), 135–146.Google Scholar
 I. Aoki, A simulation study on the schooling mechanism in fish, Bull. Jpn. Soc. Sci. Fish. 48 (8) (1982), 1081–1088.
 H. Scott Gordon, The economic theory of a common-property resource: the fishery, J. Polit. Econ. 62 (2) (1954), 124–142.
 R. Hilborn, F. Micheli and G. A De Leo, Integrating marine protected areas with catch regulation, Can. J. Fish. Aquat. Sci. 63 (3) (2006), 642–649.
 E. Ott and T. M. Antonsen, Long time evolution of phase oscillator systems, Chaos 19 (2) (2009), 023117.Web of Science
 E. Ott and T. M. Antonsen, Long time evolution of phase oscillator systems, Chaos 21 (2) (2011), 025112.Web of Science
 R. E. Mirollo, The asymptotic behavior of the order parameter for the infinite-n kuramoto model, Chaos 22 (2012), 043118.Google Scholar
 B. Birnir, Global attractors and basic turbulence, in: K. M. Spatschek and F. G. Mertens, editors,Nonlinear coherent structures in physics and biology, volume 329, NATO ASI Series, NewYork, 1994.
 J. Milnor, On the concept of attractor, Commun. Math. Phys. 99 (1985), 177–195.Google Scholar
About the article
Published Online: 2017-02-16
Published in Print: 2017-04-01