Synthesis and Computer Study of Population Dynamics Controlled Models Using Methods of Numerical Optimization, Stochastization and Machine Learning

The problems of synthesis and analysis of multidimensional controlled models of population dynamics are of both theoretical and applied interest. The need to solve numerical optimization problems for such a class of models is associated with the expansion of ecosystem control requirements. The need to solve the problem of stochastization is associated with the emergence of new problems in the study of ecological systems properties under the influence of random factors. The aim of the work is to develop a new approach to studying the properties of population dynamics systems using methods of numerical optimization, stochastization and machine learning. The synthesis problems of nonlinear three-dimensional models of interconnected species number dynamics, taking into account trophic chains and competition in prey populations, are studied. Theorems on the asymptotic stability of equilibrium states are proved. A qualitative and numerical study of the models is carried out. Using computational experiments, the results of an analytical stability and permanent coexistence study are verified. The search for equilibrium states belonging to the stability and permanent coexistence region is made using the developed intelligent algorithm and evolutionary calculations. The transition is made from the model specified by the vector ordinary differential equation to the corresponding stochastic model. A comparative analysis of deterministic and stochastic models with competition and trophic chains is carried out. New effects are revealed that are characteristic of three-dimensional models, taking into account the competition in populations of prey. The formulation of the optimal control problem for a model with competition and trophic chains is proposed. To find optimal trajectories, new generalized algorithms for numerical optimization are developed. A methods for the synthesis of controllers based on the use of artificial neural networks and machine learning are developed. The results on the search for optimal trajectories and generation of control functions are presented.The obtained results can be used in modeling problems of ecological, demographic, socio-economic and chemical kinetics systems.

Using the criterion of resistibility to assess of a structural limit state

Introduction. Subject of research: behaviour characteristics of an arbitrary structure under the loads that approach the limit load value. Goals: development of an objective and sufficiently universal methodology for the identification of the bearing capacity of a structure, which could allow to stop using any subjective assessments of their limit bearing capacity. Materials and methods. Behaviour characteristics are assessed by analyzing a curve of equilibrium states. The curve is constructed using the characteristic displacement, understood as the generalized displacement q, which energetically matches applied generalized force λ in the sense that the product of λdq is the growth of work performed by generalized force λ in respect of the growth of displacement dq. Results. The article shows that the system’s response, no matter what fixed conditions it is in, is not always sufficient for the assessment of the reliability of the system in case of the variable interaction with the environment. The co-authors use the V.V. Katyushin concept about supplementing the notion of the limit state with the characteristics of the system’s beha­viour determined by the velocity of a change in the system’s response caused by the change in the external action. According to the co-authors’ suggestion, the meter should represent the reduction in the slope of the curve of equilibrium states, which characterizes the loss of resistibility and, consequently, it can be used to assess the closeness of the structure to the state of failure, which arises if the resistibility of the system is equal to zero. The suggestion is to use the value of the slope of the curve of equilibrium states as the limit state, when the resistibility has reduced, and the velocity of deformation intensification has gone up 100 times if compared with the behaviour of an unloaded system. This suggestion is illustrated by the case of the analysis of a reinforced concrete diaphragm of a building. Conclusions. The proposed calculation methodology can be applied in the design of loadbearing structural elements, whose finite-element computational model has components that are different from the rod ones.

The K-property for some unique equilibrium states in flows and homeomorphisms

We set out some general criteria to prove the K-property, refining the assumptions used in an earlier paper for the flow case, and introducing the analogous discrete-time result. We also introduce one-sided $\lambda $ -decompositions, as well as multiple techniques for checking the pressure gap required to show the K-property. We apply our results to the family of Mañé diffeomorphisms and the Katok map. Our argument builds on the orbit decomposition theory of Climenhaga and Thompson.

Roll-over stability as a problem of high-rise buildings’ designing

Roll-over stability of tall buildings under wind loads is considered. The nonlinear nature of the problem is taken into account, including geometric, physical, and structural non-linearity. The problem is solved on the base of a system of linearized incremental equations of structural mechanics that describes the behavior of a system tall building - foundation soil. Several methods are examined for solving nonlinear problems of roll-over stability, specifically: 1) deformation method of systems equilibrium states tracing; 2) method of linearization of nonlinear equations and systems equilibrium states tracing; 3) method of linearization of nonlinear physical relations of a systems with constructive, static, geometric nonlinearity; 4) method of linearization of nonlinear physical relations of a system with constructive nonlinearity based on nonlinear incremental structural mechanics; 5) method of the deformation process tracing for a physically nonlinear soil base, given the increase of discharge zones and constructive nonlinearity. Each of these methods is used to solve a model task. These tasks take into account roll-over stability of high structures under action of wind loads. In general, the problem of roll-over stability of a high object can be represented as repeatedly nonlinear one with various types of non-linearity. In this regard, in the practice of high-rise buildings designing, it is necessary to develop scientifically and methodically substantiated methods of assessing roll-over stability, considering non-linear factors. Taking these factors into account will make it possible to assess the roll-over stability of a high-rise object more accurate.

Game-Theoretic Dynamic Procedure for a Power Index under Relative Symmetry

In many operational processes, a suitable combination of participating elements has a huge impact throughout the entire process. In the real environment, however, many combinations show less than expected results in the initial stage. In consideration of the many subjective and objective factors such as equipment, time, capital, materials, and so forth, it seems that the aforementioned combinations cannot be used to re-configure. It is important that these initial unsatisfactory combinations can gradually approach some equilibrium states or results through some rolling adjustment processes. In order to improve the above problem, this study attempts to use a game-theoretic dynamic procedure to establish a mechanism that can be dynamically modified under relative symmetry at any time during operational processes. Under such a dynamic procedure, an undesirable combination of participating elements can gradually approach a useful combination.