Establishment and Fecundity in Spatial Ecological Models: Functional Evolutions

We consider spatial population dynamics given by Markov birth-anddeath process with constant mortality and birth influenced by establishment or fecundity. The independent dispersion of spreading as well as density dependent dispersion are studied. The existence of functional evolutions for microscopic and mesoscopic descriptions of the corresponding system is shown. The Vlasov-type non-linear kinetic equations are derived and studied.

[1]  Dmitri Finkelshtein,et al.  Semigroup approach to birth-and-death stochastic dynamics in continuum , 2011, 1109.5094.

[2]  Yuri Kozitsky,et al.  Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions , 2011, 1109.4754.

[3]  Dmitri Finkelshtein,et al.  Operator approach to Vlasov scaling for some models of spatial ecology , 2011 .

[4]  Yuri Kozitsky,et al.  Glauber Dynamics in Continuum: A Constructive Approach to Evolution of States , 2011 .

[5]  Dmitri Finkelshtein,et al.  Vlasov Scaling for Stochastic Dynamics of Continuous Systems , 2010 .

[6]  Dmitri Finkelshtein,et al.  Individual Based Model with Competition in Spatial Ecology , 2008, SIAM J. Math. Anal..

[7]  Yuri Kondratiev,et al.  On non-equilibrium stochastic dynamics for interacting particle systems in continuum , 2008 .

[8]  Yuri Kondratiev,et al.  CORRELATION FUNCTIONS AND INVARIANT MEASURES IN CONTINUOUS CONTACT MODEL , 2008 .

[9]  Anatoli V. Skorokhod,et al.  ON CONTACT PROCESSES IN CONTINUUM , 2006 .

[10]  Oleksandr Kutoviy,et al.  On the metrical properties of the configuration space , 2006 .

[11]  Yuri Kondratiev,et al.  One-Particle Subspace of the Glauber Dynamics Generator for Continuous Particle Systems , 2004 .

[12]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[13]  Sergio Albeverio,et al.  Analysis and Geometry on Configuration Spaces , 1998 .

[14]  A. Lenard,et al.  States of classical statistical mechanical systems of infinitely many particles. I , 1975 .

[15]  A. Lenard,et al.  States of classical statistical mechanical systems of infinitely many particles. II. Characterization of correlation measures , 1975 .