Mathematical modelling of the evolutions of the populations in the connected two islands

Аннотация

The present paper is devoted to the investigation of the evolutions of the populations in two connected islands. The problem of the evolution of the population in one island was learnt by ecologist Robert May using the quadratic mappings. The mathematical theory of this work strictly depends on the problem of Von Neumann - Ulam. In this paper we investigate of the evolutions of the populations in two connected islands. The mathematical theory of this work depends on the two-dimensional case of the problem of Von Neumann - Ulam. We investigate the properties of the sets of Julia and Mandelbrot for the two-dimensional case of the famous mapping on the plane to itself. The sets of Julia and Mandelbrot help to define asymptotical behaviour of the trajectories of certain mappings. The analytical solutions of the equations for finding fixed and periodic points and the computational simulations for describing the sets of Julia and Mandelbrot are the main results of this paper. The asymptotical behaviours of the trajectories of certain mappings apply how change the numbers of the populations. Nowadays the most popular to learn chaotic oscillations of the real phenomena. The chaotical oscillation of numbers of population is the greatest result of this paper.