Mathematical models of ecological niches search

Abstract

This work develops mathematical models of two communities escaping the competition. Models are represented by the Cauchy problem for the system of ordinary differential equations and boundary value problems for systems of partial differential equations.

An Analytical Study of Applied Mathematical Model towards Several Ecological Systems

“…Historically, biology mathematical models have primarily been used for contextual interpretations of nature phenomena [8] [9] [10]. The attempts in order to utilize rivalry prototypes to describe genre diversity (Diamond and Case, 1986) [11] are a textbook example of this approach.…”

Msthematical Model of Operational Competition

“…On the basis of the model (2) the following models were proposed: the competition of populations in the presence of a predator [11], the competition of populations with an ecological niche [12], the competition of cellular populations [13], the competition of populations on a mobile resource [14] and other models [3].…”

“…As follows from these expressions for (12) The solution of these equations must satisfy the following conditions [2], [15], […”

Stability in the process with lag of interaction between mining and processing industries

“…A number of mathematical models describing the interaction between agents based on the game theory was considered in [6][7][8][9][10][11][12][13][14][15][16][17][18]. The results on the business security, the impact of external factors on the growth of the business are given in [19,20].…”