A Curie-Weiss Model with Dissipation

Journal of Statistical Physics

Volumn 152, Issue 1, 2013, Pages 37-53

  Dai Pra, Paolo ^a   Fischer, Markus ^a   Regoli, Daniele ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Mean field models; Noise induced periodicity; Random potential

Indexed keywords

EID: 84878801028     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-013-0756-2     Document Type: Article

References (18)

1. Budhiraja, A., Del Moral, P., Rubenthaler, S.: Discrete time Markovian agents interacting through a potential. ESAIM, Probab. Stat. (2013). doi: 10. 1051/ps/2012014.
2. Carletti, T., Villari, G.: A note on existence and uniqueness of limit cycles for Liénard systems. J. Math. Anal. Appl. 307(2), 763-773 (2005). doi: 10. 1016/j. jmaa. 2005. 01. 054.
3. Dai Pra, P., Runggaldier, W. J., Sartori, E., Tolotti, M.: Large portfolio losses: a dynamic contagion model. Ann. Appl. Probab. 19(1), 347-394 (2009). doi: 10. 1214/08-AAP544.
4. Fitzhugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445-466 (1961).
5. Garcia-Ojalvo, J., Elowitz, M., Strogatz, S.: Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. Proc. Natl. Acad. Sci. USA 101(30), 10955-10960 (2004).
6. Giacomin, G., Pakdaman, K., Pellegrin, X., Poquet, C.: Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach. SIAM J. Math. Anal. 44(6), 4165-4194 (2012). doi: 10. 1137/110846452.
7. Giesecke, K., Spiliopoulos, K., Sowers, R.: Default clustering in large portfolios: Typical events. Ann. Appl. Probab. 23(1), 348-385 (2013). doi: 10. 1214/12-AAP845. http://projecteuclid. org/euclid. aoap/1359124389.
8. Gottlieb, A. D.: Markov transitions and the propagation of chaos. In: ProQuest LLC, Ann Arbor, MI. Ph. D. Thesis, University of California, Berkeley (1998).
9. Graham, C.: McKean-Vlasov Itô-Skorohod equations, and nonlinear diffusions with discrete jump sets. Stoch. Process. Appl. 40(1), 69-82 (1992). doi: 10. 1016/0304-4149(92)90138-G.
10. Kolokoltsov, V.: Nonlinear Markov Processes and Kinetic Equations vol. 182. Cambridge University Press, Cambridge (2010).
11. Lindner, B., Garcia-Ojalvo, J., Neiman, A., Schimansky-Geier, L.: Effects of noise in excitable systems. Phys. Rep. 392(6), 321-424 (2004).
12. McMillen, D., Kopell, N., Hasty, J., Collins, J.: Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Natl. Acad. Sci. 99(2), 679-684 (2002).
13. Nagumo, J., Arimoto, S., Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. IRE 50(10), 2061-2070 (1962).
14. Pakdaman, K., Perthame, B., Salort, D.: Dynamics of a structured neuron population. Nonlinearity 23(1), 55-75 (2010). doi: 10. 1088/0951-7715/23/1/003.
15. Pakdaman, K., Perthame, B., Salort, D.: 2011, Relaxation and self-sustained oscillations in the time elapsed neuron network model. arXiv: 1109. 3014.
16. Prindle, A., Samayoa, P., Razinkov, I., Danino, T., Tsimring, L., Hasty, J.: A sensing array of radically coupled genetic 'biopixels'. Nature 481, 39-44 (2011). doi: 10. 1038/nature10722.
17. Sabatini, M., Villari, G.: Limit cycle uniqueness for a class of planar dynamical systems. Appl. Math. Lett. 19(11), 1180-1184 (2006). doi: 10. 1016/j. aml. 2005. 09. 017.
18. Schweitzer, F.: Collective Dynamics in the Natural and Social Sciences. Brownian Agents and Active Particles. Springer Series in Synergetics. Springer, Berlin (2003), with a foreword by J. Doyne Farmer.