The complex systems

The objective of this paper is to analyze the characteristics of models of a complex system of mankind. The opportunities for the actions of people and humanity are included in the model of the system. Social structures as well as the impact of humanity on the environment are excluded from the model. A small quantitative model of mankind’s system has been previously presented in my papers. The elements of small and big models are resources or resource groups. By resources, we mean tools, things, qualities, and methods that can be used to achieve human goals.
This article introduces a set of regional models in addition to small model of the humankind system.
It is shown that the proposed regional models are the models of complex systems. The characteristics of these models are considered.
This article has an interdisciplinary nature. It addresses the issues of complex systems and the history of mankind.

Abstract. The necessity and possibility to construct a holistic world picture in the conditions of on-going differentiation and specialization of modern science significantly inferior to the concomitant integration process is shown. The construction of a unified world picture is done with the help of the system-structural methodology, the main method of which is the levels of structural organization of matter providing a sequential transition as a chain from one level to another from elementary particles to the maximum space objects, including biological and social systems and back providing a law-governed sequence of transitions through the levels of structural matter organization. All this is useful for any scientific research at the initial and final stage, as well as, in an educational system.

In the paper, flows of an inhomogeneous medium consisting of gas and dispersed inclusions are simulated. The research objective is aerosols, i.e. solid particles or liquid droplets suspended in gas. The mathematical model of the complex medium flow consists of the dynamics equations for the carrier component, i.e. gas, and the dynamics equations for the dispersed component. The system of equations describing the motion of each mixture component includes continuity equations of mass, momentum and energy. The continuity of momentum for the carrier phase is described by the one-dimensional Navier-Stokes equation. The interphase interaction was defined by relations known from the literature. The mixture dynamics was simulated in one-dimensional approximation. The mathematical model equations were integrated using an explicit finite-difference method. To suppress numerical oscillations, a nonlinear grid function correction scheme was applied to the obtained solution.

The three-dimensional representation of the solution for the ordinary differential equations system (ODE) describing convective flow is a Lorentz attractor. This system of equations is the basic deterministic system with which the development of chaos theory began. In order to derive the characteristics of this complex system, the development of a modern accessible and easy to use software product is necessary.
The aim of the work was to create a program for investigating the Lorentz attractor in Python using special command libraries. Particular attention is paid to ways of solving the system of ordinary differential equations by different numerical methods and to the clarity of the presented results.
The code blocks of the developed software are described; it is used to calculate the Lorentz attractor by varying the numerical methods for solving the ordinary differential equations and system parameters. Conclusions are drawn from the results of the calculation.

The paper еtheorizes the relationship between a redshift in the electromagnetic spectrum of space objects and their gravity and demonstrates it with computational experiments. Redshift, in this case, is a consequence of deceleration of the photons emitted from the surface of objects, which is caused by the gravity of these objects. The photon speed reduction due to the attraction of space gravitating object (GO) is defined as ΔC = C-C ‘, where C’ is a photon speed changed by the time the receiver records it. Then, at photon speed variation between a stationary source and a receiver, the redshift factor is determined as Z = (C-C ‘)/C’. Computational experiments have determined the gravitational redshift of the Earth, the Sun, a neutron star, and a quasar. The graph of the relationship between the redshift and the ratio of sizes to the mass of any space GOs washas been obtained. The findings indicate that the distance to space objects does not depend on the redshift of these objects.

This paper proposes a version of the brain mechanism for emergence and formation of perceptual and mental images. The initial event of perceptual image emergence is the result of interaction on thalamic relay neurons between chaotic sensory impulse flow and also impulse flow organized in trains and coming from reticular structures. The subsequent step is the formation of a metastable dynamic association of excited allocortex columns. The role played by the functional association of allocortex columns and the intrafusal muscular reception in the activation of distributed brain systems and in the formation of a perceptual image is considered. This image is seen as a meta-stable state of synergistic processes in neuromuscular structures. The rationale for the imperceivableness of a perceptual image is given. It is assumed that a mental image is based on the perceived effects of Newtonian forces caused by muscle contractions. Properties of perceptual and mental images, their difference and conjugacy, and also the role of a mental image in interaction with conscious images are discussed.

The paper deals with the philosophical and methodological aspects of the geosystems, or geographical systems, doctrine evolution. Attention is drawn to undesirable tendencies in this evolution, manifested in giving some aspects of the doctrine the appearance of fundamental principles. It shows general scientific dialectic base of the classical variant of the geosystem doctrine as it was developed by its founder academician V. B. Sochava. It emphasizes the inconsistency of particular principles of the doctrine on geosystems as a metascientific paradigm developed later and being developed at present, the relative fundamentality and viability of the classical and widely interpreted, “imperfect” concepts, allowing to operate them in a wide range of aspects of geographical (and not only) knowledge, in particular, using the example of the geosystem doctrine.

The COVID-19 virus has claimed thousands of lives and created a global economic and social crisis.
The aim of the paper is to draw attention to the control of virus-human interactions. The following objectives are formulated. 1. To suppress (minimise) the virus activity in a human body. 2. To prevent (minimise) viral spreading while maximising economic growth. 3. Use of consciousness (dynamic stereotypes) to build protective skills against viruses, to enhance immunity and to use viruses for human benefit. 4. Statement of the problem on coexistence of a virus (biosphere) and a human. Analysis of these tasks made it possible to formulate possible solutions and to discuss implementation mechanisms: acquired and inborn skill bases, self-learning and self-organization methods and practice of conscious stereotype creation. Some of these possibilities are discussed in this paper.
The authors have developed and successfully use individual therapy based on self-regulation and the central organisation of autonomic functions. They have investigated the formation of stereotypes and dominants in animal experiments and in clinical treatment.
The main conclusion is that today the dominant focus of people’s consciousness is on the social problems of society. The inner sphere has virtually no place in people’s consciousness. It is necessary to reorient the dominant of our consciousness towards solving the problems of the internal sphere of human body in order to keep the balance. In particular, this concerns human interaction with COVID-19.

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.