The complex systems

To simulate processes of various physical and chemical nature (which is important for solving various practical problems associated with systems characterized by the occurrence of physical and chemical processes in them), the authors previously developed in the framework of modern non-equilibrium thermodynamics potential The stream method of mathematical modeling of these processes is a unified approach to the description and modeling of processes of various physical and chemical nature. The authors also considered obtaining a mathematical model of a physical and chemical system from the equations of the potential-flow method that describes the processes in this system (this model is a relationship between the output characteristics of the physical and chemical system under consideration that have practical meaning). This approach is Monte Carlo methods, according to which the factors of the flow of physical and chemical processes are randomly set, the corresponding dynamics of these processes are determined from the equations of the potential-flow method, and then the model of the system under consideration is approximated on these dynamics. Hence, to reduce the amount of computation, it is necessary to simplify this system of equations piecewise. This paper is devoted to the simplification of potential-flow equations.

The paper considers the process when a self-organized system is reaching its evolutionary maturity. The results obtained can be applied to explain orbital characteristics for five planets of the solar system. The system does not possess specifics of natural objects and is regarded as part of a structure that has borders. In its turn, the structure is understood as a network consisting of nodes (the allowed states) and connections between them. The system is formed as a deployment of a proto-structure, being a two-component cyclically organized system of relations, which is interpreted as the primary structure intended for a step-by-step study of evolution. Evolution is understood as a history-based stage-by-stage deployment. The proto-structure defines the range of the allowed states for n, the order parameter of the system, which subordinates two relative characteristics. As a result of the interaction, the elements of the specified spectrum are split into components and specialize. In this work, the initial data are derived from the analysis of the previous stage of evolution, where the splitting of ten n-nodes within one isolated cycle of the proto-structure is considered. Here we examine five n-nodes; in details, they are presented using approximately fifty interacting positions. These positions are located on three hierarchy levels: the level of positions n, as well as their splittings - the level of shifts n relative to the initial positions - the level of splitting shifts. The inter-level relations and the level of shifts are considered in detail, the basis of which is the invariants formed at the previous stage of evolution.
For application purposes, in the context of circular motion, each element of the spectrum n is interpreted as a relative angular momentum in the solar system. Otherwise, the element of the spectrum is split into components, and each of them is responsible for the subordinate distance or for the period of revolution. The evolutionary maturity of planetary distances and orbital periods

Relations between the object and the subject, the objective reality in quantum mechanics and the theory of systems are investigated. Only as a result of observation does a quantum object become either a particle or a wave. Without the role of an observer, an object can simultaneously be in many states, while not being in any of them. In essence, wave-particle duality directly contradicts the notion of the existence of «objective reality» independent of the observer. Quantum mechanics postulates the inseparability of the subject, object and their interaction, and the theory of systems determines their relationship. Material reality, neither objective nor subjective, exists. Quantum objects materialize their states depending on the conditions of observation and at the request of the observer. Objective, independent of us, the world does not exist. To one degree or another, we influence all the objects of this world, and the world affects us. Each of the interacting elements of the system contributes to the formation of the reality of the element of the system and the entire system as a whole. The more elements interact with a large number of system elements, the more «real» it is. This conclusion, however paradoxical, not only does not contradict, but also follows both from the laws of quantum mechanics and from the laws of systemology.

The article presents a brief history of the formation of representations in the category of «complexity». Modern interpretations of the term in various Sciences are shown. The system approach to understanding complexity is most fully stated.