{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:59:05Z","timestamp":1742914745150,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319690834"},{"type":"electronic","value":"9783319690841"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-69084-1_3","type":"book-chapter","created":{"date-parts":[[2017,10,5]],"date-time":"2017-10-05T23:30:06Z","timestamp":1507246206000},"page":"33-45","source":"Crossref","is-referenced-by-count":0,"title":["The Dynamics and Stability of Probabilistic Population Processes"],"prefix":"10.1007","author":[{"given":"Ioannis","family":"Chatzigiannakis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Spirakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,7]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: 23rd Annual ACM Symposium on Principles of Distributed Computing (PODC), New York, NY, USA, pp. 290\u2013299 (2004)","DOI":"10.1145\/1011767.1011810"},{"key":"3_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/11864219_5","volume-title":"Distributed Computing","author":"D Angluin","year":"2006","unstructured":"Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 61\u201375. Springer, Heidelberg (2006). doi: 10.1007\/11864219_5"},{"key":"3_CR3","unstructured":"Belleville, A., Doty, D., Soloveichik, D.: Hardness of computing and approximating predicates and functions with leaderless population protocols. In: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), Leibniz International Proceedings in Informatics (LIPIcs), vol. 80, pp. 141:1\u2013141:14, Dagstuhl, Germany (2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik"},{"issue":"46","key":"3_CR4","doi-asserted-by":"publisher","first-page":"6469","DOI":"10.1016\/j.tcs.2011.07.001","volume":"412","author":"I Chatzigiannakis","year":"2011","unstructured":"Chatzigiannakis, I., Michail, O., Nikolaou, S., Pavlogiannis, A., Spirakis, P.G.: Passively mobile communicating machines that use restricted space. Theor. Comput. Sci. 412(46), 6469\u20136483 (2011)","journal-title":"Theor. Comput. Sci."},{"issue":"1","key":"3_CR5","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.cosrev.2010.09.003","volume":"5","author":"I Chatzigiannakis","year":"2011","unstructured":"Chatzigiannakis, I., Mylonas, G., Vitaletti, A.: Urban pervasive applications: challenges, scenarios and case studies. Comput. Sci. Rev. 5(1), 103\u2013118 (2011)","journal-title":"Comput. Sci. Rev."},{"key":"3_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1007\/978-3-540-87779-0_35","volume-title":"Distributed Computing","author":"I Chatzigiannakis","year":"2008","unstructured":"Chatzigiannakis, I., Spirakis, P.G.: The dynamics of probabilistic population protocols. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 498\u2013499. Springer, Heidelberg (2008). doi: 10.1007\/978-3-540-87779-0_35"},{"key":"3_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/978-3-662-47672-7_32","volume-title":"Automata, Languages, and Programming","author":"J Czyzowicz","year":"2015","unstructured":"Czyzowicz, J., Ga\u0327sieniec, L., Kosowski, A., Kranakis, E., Spirakis, P.G., Uzna\u0144ski, P.: On convergence and threshold properties of discrete Lotka-Volterra population protocols. In: Halld\u00f3rsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 393\u2013405. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-47672-7_32"},{"issue":"1\u20132","key":"3_CR8","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1007\/BF03160228","volume":"6","author":"Z Diamadi","year":"2001","unstructured":"Diamadi, Z., Fischer, M.J.: A simple game for the study of trust in distributed systems. Wuhan Univ. J. Nat. Sci. 6(1\u20132), 72\u201382 (2001)","journal-title":"Wuhan Univ. J. Nat. Sci."},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/11494676_11","volume-title":"Engineering Self-Organising Systems","author":"A Galstyan","year":"2005","unstructured":"Galstyan, A., Lerman, K.: Analysis of a stochastic model of adaptive task allocation in robots. In: Brueckner, S.A., Di Marzo Serugendo, G., Karageorgos, A., Nagpal, R. (eds.) ESOA 2004. LNCS, vol. 3464, pp. 167\u2013179. Springer, Heidelberg (2005). doi: 10.1007\/11494676_11"},{"key":"3_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1007\/978-3-642-02930-1_40","volume-title":"Automata, Languages and Programming","author":"R Guerraoui","year":"2009","unstructured":"Guerraoui, R., Ruppert, E.: Names trump malice: tiny mobile agents can tolerate Byzantine failures. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 484\u2013495. Springer, Heidelberg (2009). doi: 10.1007\/978-3-642-02930-1_40"},{"issue":"4","key":"3_CR11","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1090\/S0002-9939-1960-0121542-7","volume":"11","author":"P Hartman","year":"1960","unstructured":"Hartman, P.: A lemma in the theory of structural stability of differential equations. Am. Math. Soc. 11(4), 610\u2013620 (1960)","journal-title":"Am. Math. Soc."},{"key":"3_CR12","volume-title":"Differential Equations, Dynamical Systems and Linear Algebra","author":"M Hirsch","year":"1974","unstructured":"Hirsch, M., Smale, S.: Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, London (1974)"},{"key":"3_CR13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary Games and Population Dynamics","author":"J Hofbauer","year":"1998","unstructured":"Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)"},{"key":"3_CR14","volume-title":"Queueing Systems, Theory","author":"L Kleinrock","year":"1975","unstructured":"Kleinrock, L.: Queueing Systems, Theory, vol. I. Wiley, Hoboken (1975)"},{"key":"3_CR15","doi-asserted-by":"crossref","unstructured":"Kurtz, T.G.: Approximation of Population Processes (1981)","DOI":"10.1137\/1.9781611970333"},{"issue":"22","key":"3_CR16","doi-asserted-by":"publisher","first-page":"2434","DOI":"10.1016\/j.tcs.2011.02.003","volume":"412","author":"O Michail","year":"2011","unstructured":"Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412(22), 2434\u20132450 (2011)","journal-title":"Theor. Comput. Sci."},{"issue":"1","key":"3_CR17","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s002240010010","volume":"34","author":"M Mitzenmacher","year":"2001","unstructured":"Mitzenmacher, M.: Analyses of load stealing models based on families of differential equations. Theory Comput. Syst. 34(1), 77\u201398 (2001)","journal-title":"Theory Comput. Syst."},{"key":"3_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813603","volume-title":"Probability and Computing: Randomized Algorithms and Probabilistic Analysis","author":"M Mitzenmacher","year":"2005","unstructured":"Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)"},{"key":"3_CR19","volume-title":"Evolutionary Game Theory","author":"JW Weibull","year":"1997","unstructured":"Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1997)"},{"key":"3_CR20","doi-asserted-by":"publisher","first-page":"1217","DOI":"10.1214\/aoap\/1177004612","volume":"5","author":"NC Wormald","year":"1995","unstructured":"Wormald, N.C.: Differential equations for random processes and random graphs. Ann. Appl. Probab. 5, 1217\u20131235 (1995)","journal-title":"Ann. Appl. Probab."}],"container-title":["Lecture Notes in Computer Science","Stabilization, Safety, and Security of Distributed Systems"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-69084-1_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T05:16:44Z","timestamp":1570166204000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-69084-1_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319690834","9783319690841"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-69084-1_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}