Исследование семейства динамических систем Спротта

A family of Sprott dynamical systems is formally defined. The main purpose of the study is formulated-modeling and analysis of the evolution of Sprott systems in relation to trading problems. The fundamental concepts and methodology for determining the symmetry, stability of systems near stationary points, dissipativity, the mutual entropy function and the fractal dimension of the generated time series are introduced. A comprehensive qualitative and quantitative study of the conservative Sprott A-system, similar to the Nose-Hoover attractor, was carried out in the Wolfram Mathematica environment. It is shown that this system demonstrates the chaotic dynamics characteristic of conservative systems and has the property of preserving the volume of the filled phase space. The curves of the evolution of the system in the phase space are constructed. A simulation study of dissipative systems similar to Lorentz and Ressler attractors is carried out. Their main parameters are determined, such as fractal dimension, dissipativity index, autocorrelation and mutual information. A generalized Sprott system H with a control parameter is investigated. The influence of the parameter on the dynamics of the system is shown. A methodology for identifying real trading systems in the class of parametric Sprot models is proposed. An example of structural and parametric identification of the dynamics of real quotations of a security of one of the issuers in the class H of the Sprot system is given.