ANALYSIS OF THE EFFICIENCY OF THE IMPLEMENTATION OF DIGITIZATION PROJECTS IN AGRICULTURAL ENTERPRISES

The article analyzes the effectiveness of the implementation of digitization projects in agricultural enterprises. The calculations take into account the uneven financial and investment opportunities of agricultural enterprises, which have provided for the differentiation of investment options depending on the funds available to the producer, as well as the actual land bank of the agricultural producer, which has affected the intensity of digitization tools. The most attractive digitization tools for agricultural enterprises in terms of implementation efficiency have been identified, among which are allocated: autopilot and course index with its subsequent installation on agricultural machinery; the system of automatic shutdown of sections of a sprayer; the system of automatic shutdown of sections of a seeder; the system of liquid fertilizer application during sowing; differentiated method of fertilization; field condition monitoring (using drones, UAVs); alternative application of fertilizers and PPE (using drones). Indicators of efficiency of realization of packages of investment projects at the land bank in 500 hectares and 5000 hectares for various options of investment (the sum of investments of 150-200 thousand UAH; 200-300 thousand UAH; 300-500 thousand UAH), and also indicators of efficiency of packages of investment projects connected with preparation and realization of production within five years of realization at the land bank of 5000 hectares for various investment options within the above amounts of investment are calculated. The most attractive sets of investment projects in digitization tools have been presented, which can be chosen by agricultural enterprises, trying to maximize the level of NPV received within certain investment opportunities. It has been determined that having different amounts of initial investment, agricultural enterprises of different sizes (with a land bank of 500 ha or 5000 ha) have a fairly wide choice of options for investing in almost every monetary segment. The expediency of investing funds of agricultural enterprises in digitization tools has been proved, which confirms the general trend towards digitization of agricultural enterprises and has a solid economic basis.

On Singular Orbits and Global Exponential Attractive Set of a Lorenz-Type System

This paper deals with some unsolved problems of the global dynamics of a three-dimensional (3D) Lorenz-type system: [Formula: see text], [Formula: see text], [Formula: see text] by constructing a series of Lyapunov functions. The main contribution of the present work is that one not only proves the existence of singularly degenerate heteroclinic cycles, existence and nonexistence of homoclinic orbits for a certain range of the parameters according to some known results and LaSalle theorem but also gives a family of mathematical expressions of global exponential attractive sets for that system with respect to its parameters, which is available only in very few papers as far as one knows. In addition, numerical simulations illustrate the consistence with the theoretical conclusions. The results together not only improve and complement the known ones, but also provide support in some future applications.

Complex Dynamical Behaviors of Lorenz-Stenflo Equations

A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

Instability of Vertical Constant Through Flows in Binary Mixtures in Porous Media with Large Pores

A binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical fluid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs are recovered. Sufficient conditions guaranteeing that a secondary steady motion or a secondary oscillatory motion can be observed after the loss of stability are found. When the layer is salted from above, a condition guaranteeing the occurrence of “cold” instability is determined. Finally, the influence of the velocity module on the increasing/decreasing of the instability thresholds is investigated.

On the Dynamics of the Chaotic General Lorenz System

In this paper, the global attractive sets of the general Lorenz system are studied based on the Lyapunov stability theory and optimization theory. The innovation of this paper lies in that the method of constructing Lyapunov functions applied to many other dynamical systems is not applicable to this general Lorenz system. Comparing with the best results in the current literature, our new results fill the gap of the estimate for the case of [Formula: see text], [Formula: see text], [Formula: see text]

Dynamical Behaviors of a Modified Lorenz–Stenflo Chaotic System

In this paper, the ultimate bound and globally exponentially attractive sets of a modified Lorenz–Stenflo system are studied based on the Lyapunov stability theory and optimization theory. Comparing with the best results in the current literature, our new results include the existing results as special cases. Furthermore, the new results offer a theoretical support to studying the Hausdorff dimension of attractor of this modified Lorenz–Stenflo system. These theoretical results are also important and useful for chaos control and chaos synchronization.