General Complex System Research Articles

Capsuled approach to analysis of the profitability of digitalization of business processes of telecommunications companies in Ukraine

Digital progress fundamentally transforms social reality, changing not only the key principles of social life but also all social institutions and spheres in which social interaction takes place, without neglecting the fundamental basis of the world's existence – the economy. Therefore, the problem of digitalization of the enterprise's business processes in the conditions of the digital economy becomes extremely urgent, given the need for high-quality management of the development of private capital.
 The purpose of the article is a multi-aspect system modeling of the encapsulated approach of the enterprise's business processes to find adequate justified management of flow processes in the conditions of digitalization of the economy. Research methodology – methods of digital analytics, based on the analysis of financial statements of enterprises and mathematical modeling of investment flows, including comparative analysis of indicators of comprehensive diagnostics of the effectiveness of digitalization of telecommunications enterprises. Findings - the key flows of business processes of enterprises are defined: material, innovative-intellectual, information-marketing, financial, the effectiveness of which management consists in the synchronization of flows with the possible assumption of temporary variations in the investment of one or another flow. Modeling made it possible to recognize the dominant flows – financial and innovative-intellectual, which allowed the authors to scientifically substantiate the need for systematic balanced management of the enterprise's business processes depending on the changing external environment, which is forced to transform intensively under the influence of the realities of the digital society. The theoretical constructs applied by the authors using the general and innovative theory of systems, the process approach of managing the quality of flows in combination with an interdisciplinary approach and analytical methodology made it possible to highlight the peculiarities of business processes in the conditions of digitalization as a general complex system that can be effectively managed using modern digital technologies.
 The study of key indicators and analysis of flow management is proposed to be carried out with the help of an encapsulated approach, which provides scientists with the basis for analytical analysis of the effectiveness of business processes at a modern enterprise in the conditions of a digital society. Research limitations – obtaining the analytical dependence of the key flows of the enterprise's business processes is a platform for making management decisions but requires the use of a more modern methodology using digital tools.

A systemic viewpoint on the approximation of a power transmission line model

This paper explains, from a systemic viewpoint, the importance to take into account the dynamic structure of the whole system in order to simplify the distributed parameters model of the transmission lines. Usually, the latter is approximated without considering its connection with the rest of the system, by comparing only its input-output behaviour with the one of the simplified model. Here, it is shown that this way to do can lead to biased results. More precisely, it is shown that the short-lines hypothesis leads to a reduction link with the π-model but does not indicate clearly which dynamics have to be kept in the simplified model as well as their number. This is illustrated by considering the voltage collapse phenomenon. From this analysis, a more systemic approximation way is proposed to reduce subsystems of a general complex system. In power systems field, all these investigations can help to improve the models used for simulation and control synthesis. Especially, to better connect the models to the specific phenomena which have to be reproduced in simulation.

Toward a systemic plant physiology

This manuscript brings a critical reflection on the epistemological foundations of the science of plant physiology. We discuss the limits of the reductionist view of the science, indicating new epistemological possibilities to plant physiology, specially based on General System Theory and Complex System paradigm, and the further implications of this major science to the human future.

Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders

A lot of progress has been made in the research of hybrid function projective synchronization (HFPS) for chaotic real nonlinear systems, while the HFPS of two different chaotic complex nonlinear systems with nonidentical dimensions is seldom reported in the literatures. So this paper discusses the HFPS of general chaotic complex system described by a unified mathematical expression with different dimensions and fully unknown parameters. Based on the Lyapunov stability theory, the adaptive controller is designed to synchronize two general uncertain chaotic complex systems with different orders in the sense of HFPS and the parameter update laws for estimating unknown parameters of chaotic complex systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Finally, the HFPS between hyperchaotic complex Lorenz system and complex Chen system and that between chaotic complex Lorenz system and hyperchaotic complex Lü are taken as two examples to demonstrate the effectiveness and feasibility of the proposed HFPS scheme.

Solving fuzzy complex system of linear equations

This paper proposes a new and simple method for solving general fuzzy complex system of linear equations. In the original system, the elements of unknown variable vector and right hand side vector are considered as complex fuzzy number. Initially the general system is solved by adding and subtracting the left and right bounds of the fuzzy complex unknown and right hand side fuzzy complex vector respectively. Subsequently above obtained solutions are used to get the final solution of the general fuzzy complex system of linear equations. Two theorems are stated and proved related to the proposed method. A mathematical example and an application problem based on electrical circuit are solved using the present method. Results obtained are compared with the known results and are found to be in good agreement.

BOUNDARY ESTIMATION OF INSPECTION THRESHOLD FOR MULTI-COMPONENT SYSTEM

Inspection threshold is one of effective methods to reduce causes of misjudgement under imperfect inspection. Based on the Bayesian theory, the threshold is defined as the boundary between inspection and noninspection execution. However, the formulation of the true threshold is difficult under a general complex system. This paper proposes approximation methods to derive the maximum and the minimum inspection thresholds for a general system. A binary reliability theory is used for the derivation of the thresholds. Structure functions, minimal path and cut sets are used for the approximation. Finally, some numerical examples are given.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type-2 intuitionistic fuzzy set(T2IFS), an entropy measure of T2 IFS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular intuitionistic trapezoidal fuzzy set(T2TITr FS) is developed, and a geometric interpretation of the T2 TITr FS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2 TITr FS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does satisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2 TITr FS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

Reliability Analysis on the $\delta$-Shock Model of Complex Systems

We investigate the delta-shock model of complex systems consisting of n i.i.d. components. We first obtain a general lifetime distribution for the delta-shock model of a general complex system by reducing the system to a linear combination of parallel systems. We then consider coherent system structures including series, parallel, and k-out-of-n, then derive some useful results including reliability bounds, bounds on the mean lifetime, limiting distributions, and Laplace-Stieltes transforms

Prediction of vibration of rotating damped beams with arbitrary pretwist

A solution procedure for the bending–bending vibration of a rotating damped beam with arbitrary pretwist and an elastically restrained root is derived. The viscous damping is assumed to be proportional to the distributed mass. The general complex system is divided into two subsystems. The physical meanings of the subsystems are studied. The exact complex frequency relations between two viscously damped beams with arbitrary pretwist and elastic root are revealed. The underdamping, critical damping and overdamping systems are analyzed. Moreover, the influence of the parameters on the decay rate, the natural frequencies, the critical damping, and the phenomenon of divergence instability are investigated.

Rank Robustness of Complex Matrices with Respect to Real Perturbations

This paper examines the problem of computing a minimum norm real matrix perturbation that causes a general complex (system) matrix to drop rank. Given the state model describing a linear time-invariant system, the norm of this matrix perturbation helps to determine the robustness of several system properties with respect to real parameter variations. The norm of this perturbation, or the real-restricted singular value of the complex matrix, is known to be a discontinuous function of the complex matrix. The paper presents a simple condition on the complex matrix that eliminates this discontinuity. Specifically, the paper shows that the size of the smallest real rank-reducing perturbation is a continuous function of the complex matrix as long as the imaginary part of the complex matrix has full rank. The paper examines other aspects of the continuity of the problem. It also presents an algorithm that converges to a point satisfying a necessary condition for obtaining the smallest real rank-reducing matrix perturbation. A Lyapunov function approach is used to establish convergence of the algorithm. Some numerical examples are included illustrating the accuracy of the approach.

Reliability Prediction Techniques for Complex Systems

As electronic systems continue to evolve into more and more complex structures, the search for better and more efficient reliability prediction techniques naturally takes on added momentum. Needed are not only systematic methods of mathematical model building that will simplify the procedures involved but also noncomplex ways of obtaining solutions to many practical problems. This paper illustrates the applicability of transition diagram in describing the state space of a complex system, repairable or nonrepairable, and shows the methodology of writing the set of first-order linear differential equations representing the system performance by inspection of the transition diagram. A discussion of some applicable properties of linear signal-flow graphs is included. Methods of solving problems by inspection techniques are clearly explained and specific examples are given to illustrate the concepts. The mean time Tm for a system to pass for the first time from its initial state to a failed state is usually a statistic of prime interest. Certain properties of Laplace transform are used to illustrate how Tm of a general complex system, repairable or nonrepairable, can be obtained by solving a set of simultaneous algebraic equations. Flow graph techniques of solution by inspection are shown to be a valuable tool in obtaining analytical solutions for Tm of many practical systems.