DECOMPOSITION METHOD FOR A COMPLEX NONLINEAR SYSTEM BASED ON A PROCESS APPROACH

В работе представлен метод декомпозиции сложных нелинейных систем с использованием процессного подхода. Показаны основные ограничения и условия применения метода к нелинейным системам различной природы и сложности. В предложенном методе процессы являются объектами управления, что позволяет усилить контроль за ними для получения наилучших результатов и повышения эффективности функционирования и прогнозирования работы нелинейной системы. The paper presents a method of decomposition of nonlinear systems with the ability to self-organization using the process approach. The main limitations and conditions for applying the method to nonlinear systems of various nature and complexity are shown. In the proposed method, the processes are objects of control, which allows you to strengthen control over them to obtain the best results and improve the efficiency of functioning and forecasting the operation of a nonlinear system.

CONCEPTUAL MODEL OF SYSTEM DEVELOPMENT STRATEGY MANAGEMENT FROM THE POSI-TION OF PROJECT APPROACH

The purpose of the article is to build a conceptual model of strategic project management through the prism of a multidisciplinary approach. Project management methodologies for the place of strategic management of complex nonlinear system development are analyzed. Standardized, adaptive and combined project and program management methodologies (PMBoK, P2M, PRINCE2, MSP, Agile) are considered. The authors pay special atten-tion to the study of the influence of the external environment on a complex nonlinear system in the context of a synergetic approach. The main part describes the process of expanding the scope of project management and inte-gration of project management with modern methods and tools of other management disciplines. Elements of the theory of synergetics and the classical theory of the design approach to the management of the development of a complex nonlinear system are synthesized. The necessity of clear definition by the team of the project of the struc-tural attractor, ie the direction of strategic development of the system is substantiated. The tool for determining compliance with the contextual requirements of SMART-goals of alternative scenarios for strategic development projects is considered. The tool of the Ishikawa diagram is used to determine the most influential factors on possi-ble deviations of the project from the strategic development of a complex nonlinear system. The conducted theoret-ical research allowed the authors to build a conceptual model of system development strategy management from the standpoint of the project approach. The conceptual model of strategic project management is constructed, the principles of its work and its use in discrete systems for actualization of administrative decisions in the conditions of risk and uncertainty are resulted. The expediency of using this conceptual model in managing the integration of strategic development projects is substantiated. Keywords: strategy, project management, program, project, synergetic, bifurcation.

Solution of Nonlinear Systems of Equations via Metaheuristics

A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system.

The RWST, a comprehensive statistical description of the non-Gaussian structures in the ISM

The interstellar medium (ISM) is a complex nonlinear system governed by the interplay between gravity and magneto-hydrodynamics, as well as radiative, thermodynamical, and chemical processes. Our understanding of it mostly progresses through observations and numerical simulations, and a quantitative comparison between these two approaches requires a generic and comprehensive statistical description of the emerging structures. The goal of this paper is to build such a description, with the purpose of permitting an efficient comparison that is independent of any specific prior or model. We started from the wavelet scattering transform (WST), a low-variance statistical description of non-Gaussian processes, which was developed in data science and encodes long-range interactions through a hierarchical multiscale approach based on the wavelet transform. We performed a reduction of the WST through a fit of its angular dependencies. This allowed us to gather most of the information it contains into a few components whose physical meanings are identified and describe for instance isotropic and anisotropic behaviours. The result of this paper is the reduced wavelet scattering transform (RWST), a statistical description with a small number of coefficients that characterizes complex structures arising from nonlinear phenomena, in particular interstellar magnetohydrodynamical (MHD) turbulence, independently of any specific priors. The RWST coefficients encode moments of order up to four, have reduced variances, and quantify the couplings between scales. To show the efficiency and generality of this description, we applied it successfully to the following three kinds of processes that are a priori very different: fractional Brownian motions, MHD simulations, and Herschel observations of the dust thermal continuum in a molecular cloud. With fewer than 100 RWST coefficients when probing six scales and eight angles on 256 by 256 maps, we were able to perform quantitative comparisons, infer relevant physical properties, and produce realistic synthetic fields.

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Another chaotic nonlinear Lü model with complex factors is covered here. We can build this riotous complex system when we add a complex nonlinear term to the third condition of the complex Lü system and think of it as if every one of the factors is mind boggling or complex. This system in real adaptation is a 6-dimensional continuous autonomous chaotic system. Different types of chaotic complex Lü system are developed. Also, another sort of synchronization is presented by us which is simple for anybody to ponder for the chaotic complex nonlinear system. This sort might be called a complex antilag synchronization (CALS). There are irregular properties for CALS and they do not exist in the literature; for example, (i) the CALS contains or fused two sorts of synchronizations (antilag synchronization ALS and lag synchronization LS); (ii) in CALS the attractors of the main and slave systems are moving opposite or similar to each other with time lag; (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A scheme is intended to accomplish CALS of chaotic complex systems in light of Lyapunov function. The acquired outcomes and effectiveness can be represented by a simulation case for our new model.