Ordinary differential equation system for population of individuals and the corresponding probabilistic model

Mathematical and Computer Modelling

Volumn 49, Issue 7-8, 2009, Pages 1551-1562

  Mamontov, E ^a  

^a UNIVERSITY OF GOTHENBURG   (Sweden)

Author keywords

Generalized kinetic theory; Ordinary differential equation; Population of individuals; Probabilistic population dynamics; Statistical approximation

Indexed keywords

DISTRIBUTION FUNCTIONS; INTEGRAL EQUATIONS; KINETIC THEORY; MEATS; ORDINARY DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; PROBABILITY DENSITY FUNCTION; STATISTICAL MECHANICS;

ACTIVE PARTICLES; FINITE SYSTEMS; GENERALIZED KINETIC THEORY; HAMILTON; INTEGRAL TERMS; KEY MODELS; KINETIC EQUATIONS; MEAN FIELDS; PARTICLE POPULATIONS; PARTICLE STATE; PHASE SPACES; POPULATION OF INDIVIDUALS; PROBABILISTIC MODELS; PROBABILISTIC POPULATION DYNAMICS; PROBABILITY THEORIES; STATE VECTORS; STATISTICAL APPROXIMATION; STOCHASTIC MECHANICS;

POPULATION STATISTICS;

EID: 60949090928     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.09.010     Document Type: Article

References (15)

1. Balescu R. Statistical Dynamics: Matter out of Equilibrium (1997), Imperial College Press, London
2. DeAngelis E., and Delitala M. Modelling complex systems in applied sciences: Methods and tools of the mathematical kinetic theory for active particles. Math. Comput. Modelling 43 (2006) 1310-1328
3. Bellomo N., Bellouquid A., Nieto J., and Soler J. Multicellular biological growing systems: Hyperbolic limits towards macroscopic description. Math. Models Methods Appl. Sci. 17 1 supp 2007 (2007) 1675-1692
4. Bellomo N. Modeling complex living systems. A Kinetic Theory and Stochastic Game Approach (2008), Birkhäuser, Boston
5. Bellomo N., Mamontov E., and Willander M. On the generalized kinetic modelling of a multi-component "real-life" fluid by means of a single distribution function. Math. Comput. Modelling 38 (2003) 637-658
6. Willander M., Mamontov E., and Chiragwandi Z. Modeling living fluids with the subdivision into the components in terms of probability distributions. Math. Models Methods Appl. Sci. 14 10 (2004) 1495-1520
7. Mamontov E., Psiuk-Maksymowicz K., and Koptioug A. Stochastic mechanics in the context of the properties of living systems. Math. Comput. Modelling 44 7-8 (2006) 595-607
8. E. Mamontov, Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory, in: 10th Evolutionary Biology Meeting at Marseilles, 20-22 September, 2006, Association pour l'Etude de l'Evolution Biologique, Centre Régional de Documentation Pédagogique, Marseille, France, (2006), pp. 28-29, abstract; the 13-page PDF file for the oral presentation is downloadable from http://www.up.univ-mrs.fr/evol-cgr/home_page/meeting2006.php
9. Mamontov E. Modelling homeorhesis by ordinary differential equations. Math. Comput. Modelling 45 5-6 (2007) 694-707
10. Piotrowska M., Mamontov E., Peterson A., and Koptyug A. A model and simulation for homeorhesis in the motion of a single individual. Math. Comput. Modelling 48 7-8 (2008) 1122-1143
11. Reichl L.E. A Modern Course in Statistical Physics (1998), John Wiley & Sons
12. Liboff R.L. Kinetic Theory: Classical, Quantum, and Relativistic Description (1998), John Wiley & Sons, New York
13. Sedov L.I. A Course in Continuum Mechanics Vol. 1 (1971), Wolters-Noordhoff, Groningen
14. Mamontov E. Dynamic-equilibrium solutions of ordinary differential equations and their role in applied problems. Appl. Math. Lett. 21 4 (2008) 320-325
15. Español P., and Warren P. Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30 4 (1995) 191-196