Investigations of complex systems' dynamics, based on reduced amount of information: introduction to the method

Controlling dynamics of complex systems is one of the most important issues in science and engineering. Thus, there is continuous need to study and develop numerical algorithms of control methods. In this paper, we would like to present our introductory study of a new simple method of investigations of such systems based on vector field properties and reduced amount of applied information. Firstly, we present the basis of our approach for extraction of nonlinear indicators of two-dimensional systems. We show that basing on simplified analyses and exploiting half of commonly applied information, we can precisely estimate widely applied indicators. We prove that our method is simpler, more efficient and more accurate than commonly applied algorithms. After the introductory analysis, we extend our studies and apply the presented method in investigations of complex systems, based on the analysis that we discussed in the first part of the article and carried out in two-dimensional subspaces. We present simplicity and effectiveness of our approach and demonstrate how it simplifies investigations of complex dynamical phenomena. We verify our method studying the example of synchronization and chimera phenomena in the chosen set of coupled oscillators.