A Chaotic Quadratic Bistable Hyperjerk System with Hidden Attractors and a Wide Range of Sample Entropy: Impulsive Stabilization

Hidden attractors generated by the interactions of dynamical variables may have no equilibrium point in their basin of attraction. They have grabbed the attention of mathematicians who investigate strange attractors. Besides, quadratic hyperjerk systems are under the magnifying glass of these mathematicians because of their elegant structures. In this paper, a quadratic hyperjerk system is introduced that can generate chaotic attractors. The dynamical behaviors of the oscillator are investigated by plotting their Lyapunov exponents and bifurcation diagrams. The multistability of the hyperjerk system is investigated using the basin of attraction. It is revealed that the system is bistable when one of its attractors is hidden. Besides, the complexity of the systems’ attractors is investigated using sample entropy as the complexity feature. It is revealed how changing the parameters can affect the complexity of the systems’ time series. In addition, one of the hyperjerk system equilibrium points is stabilized using impulsive control. All real initial conditions become the equilibrium points of the basin of attraction using the stabilizing method.

Thermodynamic modeling of iron recovery processes

One of the promising directions in metallurgy is the use of iron-containing waste, such as converter production sludge, iron-containing concentrates, rolling scale, iron ore processing waste and others. Development of new resource-saving technologies using such waste requires preliminary research and accumulation of information in the field of iron recovery. The paper considers the processes of iron recovery from oxides under various conditions. The authors used the method of thermodynamic modeling based on the search for the entropy maximum. The thermodynamic modeling tool was TERRA software package created at the Bauman Moscow State Technical University. TERRA complex is designed to calculate the thermodynamic properties and composition of the phases of equilibrium state of arbitrary systems with chemical and phase transformations. Using this software package, studies of the processes of iron recovery by various reducing agents (carbon, manganese, and silicon) in model thermodynamic systems were carried out, and optimal conditions for temperature and consumption of reducing agents were determined. The paper presents the results of a study of processes in the metal-slag system in equilibrium. The analysis of the metal-slag system equilibrium state was carried out for the temperature range of 1773 - 1973 K with different amounts of slag. Boundaries of the areas of redox processes were determined and the influence of metal components on conditions for iron oxides recovery from slag to metal was evaluated. The dependences of the system equilibrium composition on temperature at different ratios of metal and slag were obtained, as well as the optimal conditions for iron recovery.

Error Estimation of Euler Method for the Instationary Stokes–Biot Coupled Problem

In this paper, we study a finite element computational model for solving the interaction between a fluid and a poroelastic structure that couples the Stokes equations with the Biot system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is used to impose weakly this condition. With the obtained finite element solutions, the error estimators are performed for the fully discrete formulations.

INVESTIGATION OF THE IMPACT OF DELAY IN ONE MATHEMATICAL MODEL OF WORLD DEVELOPMENT DYNAMICS

There is a large number of works devoted to the dynamics of world development. But very few of them have clear abstract mathematical models of the corresponding processes. This work is devoted to further deepening and mathematical abstraction of the study of world development process. The qualitative analysis of linear and modified nonlinear model in the form of systems of inhomogeneous differential equations is carried out. Their steady states are calculated, explicit analytical solutions are presented. For the first time, a model taking into account the time delay factor is proposed, which is written in the form of functional-differential equations with argument deviation. It is shown that with such an introduction to the model of a delayed argument, the system can be reduced to a system of linear inhomogeneous differential equations with constant coefficients without delay, and the stability of the steady state of the system equilibrium under study will be affected only by linear terms of equations without argument deviation. This fact well correlates with the socio-economic interpretation of this problem. In the future, the work will focus on studying the influence of not one but several factors of time lag, when the model is presented as a system of functional-differential equations with several different deviating arguments in equations responsible for the dynamics of a particular process dynamics of world development.

«COMPLЕXITY» AND «PERPLEXITY» – CATEGORIES OF DEVELOPMENT OF GOVERNANCE SYSTEMS

Addressing the issue of «complexity» and «perplexity» categories is caused by the evolution of system types ranging from well-organized to self-organizing, expanding the horizons of scientific rationality. Development of governance systems is revealed through the dichotomy of properties and restrictions within the «organizational set-up» and «external influence» notions. It was shown that the governance system falls into the category of complexity because the system is operating on the edge of «order and chaos». External environment is presented as chaos analogue showing uncertainty and changes of various fluctuation category, up to turbulence. The incorporation of social and economic system into external environment was considered from the perspective of formation of «system convergence» of two open systems, contributing to growth of the degree of complexity of governance system. It was emphasized that business development forces perplexity governance systems to switch to robust control; the mechanism of robust control is organized under the influence of the laws of evolution and survivability of biosystems. The following methods were marked out and justified: selection of parameters for system convergence of governance system with external environment entities, determination of limits of information granules of adaptive and robust homeostasis, scenario planning, construction of convergent strategy and temporal attractor of system equilibrium state, known as «floating equilibrium». These methods are to be mastered by the governance system within robust control.

Consistent Modelling of Non-Equilibrium Thermodynamic Processes in the Atmosphere

<p>Approximations in the moist thermodynamics of atmospheric/weather models are often inconsistent. Different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. In order to address these problems we may derive all relevant thermodynamic quantities from a defined thermodynamic potential; approximations are then instead made to the potential itself --- this guarantees self-consistency. This concept is viable for vapor and liquid water mixtures in a moist atmospheric system using the Gibbs function but on extension to include the ice phase an ambiguity exists at the triple-point. In order to resolve this the energy function must be used instead; constrained maximisation methods may be used on the entropy in order to solve the system equilibrium state. Once this is done however, a further extension is necessary for atmospheric systems. In the Earth's atmosphere many important non-equilibrium processes take place; for example, freezing of super-cooled water, evaporation, and precipitation. To fully capture these processes the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. This may be done using various principles of non-equilibrium thermodynamics, principally Onsager reciprocal relations. A numerical scheme may then be implemented which models the competing finite processes in a moist thermodynamic system.</p>