Application of the Nonlinear Oscillations Theory to the Study of Non-equilibrium Financial Market

Abstract

The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium financial market. View of the dynamic variables data was determined based on the strength of econophysical prerequisites using the model of hydrodynamic type. As a result, we found that the non-equilibrium market can be described with a good degree of accuracy with oscillator models with nonlinear rigidity and a self-oscillating system with inertial self-excitation. The most important states of model of oscillation non-equilibrium model of the market were found, including the appearance of chaos and its mechanisms. We have made the calculations of the correlation dimension for the financial time series. The results show that all observed time series have a clearly defined chaotic dynamic nature.

Power series approach to nonlinear oscillators

“…5 Several important oscillators with important applications in physics and engineering have attracted the attention of many researches. [12][13][14][15][16][17] For example, the excited spring pendulum has been studied well using the so-called multi-scale method, in which the authors obtained approximate solutions of the equations of motion of the system. 12,13 Furthermore, the Van-der Pol and Duffing oscillators have been considered in many works.…”

“…[12][13][14][15][16][17] For example, the excited spring pendulum has been studied well using the so-called multi-scale method, in which the authors obtained approximate solutions of the equations of motion of the system. 12,13 Furthermore, the Van-der Pol and Duffing oscillators have been considered in many works. [13][14][15][16][17] In these references, one can see that the Van-der Pol oscillator was analyzed using some perturbation techniques to obtain approximate solution to its dynamical equations.…”