|
Conference publicationsAbstractsXX conferenceMathematical modeling of the northern deer population dynamics2 Institutskaya st., Puschino, 142290, Russia 140 Vavilov st., Moscow, 119333, Russia
The discrete mathematical model of the dynamics of a non-operating group of reindeer is considered in [1]. This model is based on relationship of population with forage resources and takes into account the age structure of the specimens. The simulation showed that the dynamics is cyclical with the oscillation period of 35-40 years; the number climbs lasting 25-30 years alternate with the decrease in the number (10 years). The real population dynamic is played well. This work is different from [1] because it can play the same dynamic modes without considering the age structure. We solve numerically the non-autonomous system of two ordinary differential equations of the first order, built on the basis of the classical Lotka-Volterra model. There are three modes in the simulation model: the food is enough (increasing population), the food is not enough (fertility is zero), the food is not available (high mortality, reduced population). In this model there is one expert function formalizing the assumption of critical levels of vegetation [2]. Taking into account the analysis of numerical experiments with the simulation model, the additional assumptions that simplify the simulation model to the analysis are introduced. The analytical solution for given system of differential equations is obtained, it has a simple form when food is not available, but if there is sufficient food supply, solution is expressed in terms of the Bessel functions [3]. The analytical solution can be an instrument settings of simulation for a more sophisticated form of expert functions.
References 1. Lopatin V.N., Abaturov B.D. Mathematical modeling of trophically induced cyclic population of reindeer (RANGIFER TARANDUS) / / Zoological Journal Volume 79, Number 4, 2000. Pp. 452-460. 2. Abaturov B.D. On the mechanisms of natural regulation of the relationship of herbivorous mammals and vegetation / / Zoological Journal, Volume 54, Number 5, 1975. Pp. 342-351. 3. Zaitsev V.F., Polyanin A.D. Handbook of Nonlinear Partial Differential Equations - Moscow: Nauka, 1993. 464 p.
|
