Study of Behavior for Non-Linear Dynamic System of Stability in Average Company

In the article nonlinear dynamical Shapovalov system as a model of stability in Average company is analyzed in the respect of its stable and chaotic behavior. The parameters and variables of the model accept economic interpretation. The system describes the correspondence changes between values of credits, capital and employment in the process of average firm’s production. The analysis focuses on the finding area of parameters when Shapovalov system tends to demonstrate stable behavior. Moreover, using special method of Lyapunov function it is computed exact Lyapunov dimension for case of system’s chaotic behavior. The result of the research is going to be the set of theorems about conditions on parameters which make system be stable or not. For concrete values of system’s parameters strange attractors are constructed. For σ=4.1, δ=1.2, α =5, γ= 1.5, μ=2.1 Shapovalov system has Lorenz-type strange attractor. The economic interpretation of mathematical dynamic model let us apply special mathematical methods for analyzing system in the field of economics that rises interest among specialists for further studying the theory of nonlinear dynamic systems’ stability. Keywords: Shapovalov system, stability, Lyapunov function, Lyapunov dimension, strange attractor.