Maria Davidich
Scientific research
Science supervisor professor Dr. A.Yu.Loskutov
What else besides chaos, appealing to internal
forces for giving the shape of the one leaf.
Conrad Iken.
Nowadays dynamical systems with chaotic behavior is attracting more and more attention. The reason for an increasing interest is that, a chaotic behavior is rather general property of different non-linear processes, which take place in various scientific disciplines, such as physics, biology, chemistry, economics and est. Appearing of the chaos is connected with internal peculiarity of the dynamical system, when with certain values of parameters the trajectories are starting to perform exponential instability.
That's why in last decade new branch of theory of deterministic chaos, which is control and suppressing of chaos (or stabilizing chaotic behavior) attracts the attention of scientific community. A chaotic dynamics is conveniently distributed by means of an external perturbation (usually small as compared with the unperturbed dynamics), in order to force to appearance of a goal behavior. Moreover it appeared, that this branch has a lot of important practical applications in real systems such as communicating with chaos, secure communication processes, and experimental control of chaos in many areas as, chemistry, biology (in cardiac rhythm), laser physics, electronic circuits, mechanical systems and economics.
It is generally accepted that economy belongs to extremely complex systems and from physics point of view both deterministic and stochastic descriptions are needed to describe main features of its dynamics. On the other hand, controlling of at least some economical processes seems to be one of the most important and challenging tasks facing the economics and politicians responsible for economical policy.
An instable situation on the market is very widespread and working in these conditions it is difficult to predict what is necessary to do in the next moment and what kind if strategy for the firm would be the most effective. So it is of vital importance for the firms to find a way for stabilization situation on the market, in order to perform the effective strategy and the increase the profit.
We developed a method allows to realize the stabilization of chaotic dynamic in micro-economical model. We show that by means of weak external direct parametric excitations it is possible to suppress chaos and stabilize prescribed periodical orbits .As control parameters we choose such values that describe the investment values of both firms. With economical points of view this means, that we may realize a quite simple control and present a way of increasing profit.