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Mathematical Biosciences and Engineering (MBE)
 

Equilibrium solutions for microscopic stochastic systems in population dynamics
Pages: 777 - 786, Issue 3, June 2013

doi:10.3934/mbe.2013.10.777      Abstract        References        Full text (368.4K)           Related Articles

MirosŁaw Lachowicz - Institute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 Warsaw, Poland (email)
Tatiana Ryabukha - Institute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 Warsaw, Poland (email)

1 L. Arlotti and N. Bellomo, Solution of a new class of nonlinear kinetic models of population dynamics, Appl. Math. Lett., 9 (1996), 65-70.       
2 L. Arlotti, N. Bellomo and M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Phys., 29 (2000), 125-139.       
3 N. Bellomo and G. Forni, Dynamics of tumor interaction with the host immune system, Math. Comput. Modelling, 20 (1994), 107-122.
4 N. Bellomo, N. K. Li and Ph.K. Maini, On the foundations of cancer modelling: Selected topics, speculations and perspectives, Math. Models Methods Appl. Sci., 18 (2008), 593-646.       
5 I. D. Chase, Models in hierarchy formation in animal societies, Behavioural Sciences, 19 (1974), 374-382.
6 E. Jäger and L. Segel, On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math., 52 (1992), 1442-1468.       
7 E. Geigant, K. Ladizhansky and A. Mogilner, An integro-differential model for orientational distribution of $F$-actin in cells, SIAM J. Appl. Math., 59 (1998), 787-809.       
8 K. Kang, B. Perthame, A. Stevens and J. J. L. Valázquez, An integro-differential model for alignment and orientational aggregation, J. Diff. Eqs., 246 (2009), 1387-1421.       
9 M. Lachowicz, Links between microscopic and macroscopic descriptions, in "Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic" (eds. V. Capasso and M. Lachowicz), in Lecture Notes in Mathematics, 1940, Springer, (2008), 201-268.       
10 M. Lachowicz, Microscopic, mesoscopic and macroscopic descriptions of complex systems, Prob. Engin. Mech., 26 (2011), 54-60.
11 M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology, Nonlinear Analysis Real World Appl., 12 (2011), 2396-2407.       
12 M. Lachowicz and D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11 (2001), 1375-1390.       
13 I. Primi, A. Stevens and J. J. I. Velázquez, Mass-selection in alignment model with non-deterministic effect, Comm. Partial Diff. Eqs., 34 (2009), 419-456.       
14 G. Theraulaz, E. Bonabeau and J.-L. Deneubourg, Self-organization of hierarchies in animal societies: the case of the primitively eusocial wasp Polistes dominulusChrist, J. Theoret. Biol., 174 (1995), 313-323.
15 E. O. Wilson, "Sociobiology: The New Synthesis," Harvard University Press, Cambridge, 1975.

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