PROGRAMS FOR CALCULATING A DYNAMIC MODE MAP ON THE EXAMPLE OF A SYSTEM WITH CHAOTIC MODES

Background . Dynamic mode maps are a visualization tool used to analyze and classify the behavior of complex nonlinear dynamic systems as parameters change. They allow us to identify how the system's operating mode (steady state, periodicity, chaos, etc.) changes when one or more parameters are varied. Materials and Methods . The paper proposes algorithms for constructing dynamic mode maps based on the convergence of periodicities and the minimum value function. The first is based on selecting the last element of the set and comparing this element in turn with all the previous ones. If the last element coincides with the previous one, then it is stated that the resulting set has a period of 1, which means that with these parameters, the system has a limit point. The second algorithm is based on creating arrays of standard deviations. Software has been developed for constructing dynamic mode maps using the convergence of periodicities and the minimum value function. Results and Discussion. Based on the analysis of dynamic mode maps obtained by these methods under the condition of the existence of the Lifshitz invariant at n = 3, it was established that the method of periodicity convergence more fully describes the existing dynamics of the incommensurate superstructure, which is experimentally traced in tetramethylammonium tetrachlorocuprate crystals. It is shown that the dynamic mode maps calculated by the method of periodicity convergence have a significant number of existing periodicities and most fully describe the dynamics of the incommensurate superstructure. It is established that the palette of existing periodicities is more represented under the condition when the increment of the phase function acts as the arguments of the recurrent relations. The dynamic mode map deserves special attention when the increment of both the amplitude and phase functions acts as the arguments of the recurrent relations. Conclusion. It has been established that the considered algorithm for constructing dynamic regime maps is effective for analyzing the dynamics of an incommensurate superstructure, which is described by a system of differential equations, and the appearance of an incommensurate superstructure is due to the existence of the Lifshitz invariant. Keywords : dynamical regime maps, incommensurate superstructure, incommensurate superstructure regimes, anisotropic interaction.