Qualitative analysis of Selkov's fractional dynamical system with variable memory using a modified Test 0-1 algorithm

The article examines chaotic and regular modes of a fractional dynamic Selkov system with variable memory. First, a numerical analysis is carried out using the Adams-Bashforth-Moulton method. Next, preliminary processing (modification) is carried out on the resulting solution, which consists of selecting from the given values the values corresponding to local extrema. Next, the set of values thinned out in this way is fed to the input of the Test 0-1 algorithm. The main idea of the Test 0-1 algorithm is to calculate the statistical characteristics of a discrete time series: the standard standard deviation, as well as its asymptotic growth rate through the correlation (covariance and variation) between the corresponding vectors. As a result, after repeatedly calculating the correlation coefficient, its median value is selected, which is the main criterion for choosing a dynamic mode scenario. If the median value is close enough to one, then we are dealing with a chaotic regime, and if it is close to zero, then with a regular regime. The Adams-Bashforth-Moulton numerical algorithm and the modified Test 0-1 algorithm were implemented in the computer mathematics system MATLAB, and the simulation results were visualized using bifurcation diagrams. In the work, it was shown using the modified Test 0-1 algorithm that a fractional dynamic system with variable memory can have chaotic modes. This is very important to know due to the fact that Selkov's fractional dynamic system describes a self-oscillating regime, which, for example, can be used to describe the interaction of microseisms. In this case, chaotic modes must be eliminated by selecting appropriate values of system parameters.