Class Of Differential Systems Research Articles

Equivalence between nonlinear dynamical systems and urn processes

An equivalence is shown between a large class of deterministic dynamical systems and a class of stochastic processes, the balanced urn processes. These dynamical systems are governed by quasi-polynomial differential systems that are widely used in mathematical modeling while urn processes are actively studied in combinatorics and probability theory. The presented equivalence extends a theorem by Flajolet et al (2006 Discrete Mathematics and Theoretical Computer Science, AG (DMTCS Proc.) pp 59–118) already establishing an isomorphism between urn processes and a particular class of differential systems with monomial vector fields. The present result is based on the fact that such monomial differential systems are canonical forms for more general dynamical systems.

ALGORITHM FOR SYNTHESIZING PARAMETERS OF CONTROL LAWS OF TECHNICAL SYSTEMS UNDER POLYNOMIAL APPROXIMATION OF NONLINEARITIES

The paper considers the algorithm for solving the problem of synthesis of automatic control systems (ACS) with nonlinear characteristics for polynomial approximation. As a mathematical apparatus, the inversion of the direct variational method of analysis, Galerkin generalized method, is applied to the solution of the problem. Recurrence relations are obtained that make it possible to extend this method to a new class of dynamical systems with nonlinear elements whose characteristics are approximated polynomially. The advantages and disadvantages of various methods of approximation of automatic control systems with nonlinear characteristics are analyzed. The presented algorithm of the software complex is universal and allows solving the synthesis problem for control systems of different classes and structures from unified mathematical, methodological and algorithmic positions.

Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.

The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions

We discuss the uniqueness of the solution to a class of differential systems with coupled integral boundary conditions under a Lipschitz condition. Our main method is the linear operator theory and the solvability for a system of inequalities. Finally, an example is given to demonstrate the validity of our main results.

Complexity–entropy causality plane based on power spectral entropy for complex time series

The complexity–entropy causality plane based on permutation entropy is a powerful tool to discriminate signals from different systems. In this paper, we combine traditional statistical complexity measure and power spectral entropy and construct complexity–entropy causality plane in frequency domain. The power spectral entropy is derived from Fourier transformation, so some features that are obscure in time domain can be extracted in frequency domain. Comparing to permutation entropy, this method is free of parameters. Several time series generated from different classes of systems are analyzed to demonstrate the measure. Results show that these signals can be clearly distinguished in our plane. Then by adding sinusoidal abnormal signal into original one, the abnormal information can be efficiently detected. Finally, we apply it to bearing vibration signals. Empirical consequences illustrate that the start–stop time and classification of fault signal can be clearly determined.

On the Asymptotic Stability Problem for Solutions of Difference Switched Systems

We consider difference systems obtained by discretizing certain classes of differential systems. It is assumed that the system under consideration can operate in several modes. The problem is to establish conditions that guarantee the asymptotic stability of a given equilibrium position when switching regimes. We use the method of Lyapunov functions. We study the case when solutions of the system under various operating modes can have features of both linear and nonlinear behavior.

Characterization of polymer electrolytes by dielectric response using electrochemical impedance spectroscopy

Abstract Authors present a phenomenological view on dielectric relaxation in polymer electrolytes, which is monitored by electrochemical impedance spectroscopy. Molecular interaction of polymer chains with salt molecules (or dipole-dipole interaction between segments and salt molecules) leads to dipolar molecular entities. Frequency-dependant impedance spectra are the key quantities of the interest for determination of electric properties of materials and their interfaces with conducting electrodes. Salt concentration serves as parameter. Bulk and interfacial properties of the samples are discussed in terms of impedance (Z *) and modulus (M *) spectra. We focus on two different classes of systems, i.e. high molar mass of poly(ethylene oxide) (PEO)+lithium perchlorate (LiClO4) (i.e. the inorganic salt) and epoxidized natural rubber (ENR-25) with 25 mol% of epoxide content+LiClO4. Impedance spectra with salt content as parameter tell us that we have interaction between dipolar entities leading to dispersion of relaxation times. However, as scaling relations show, dispersion of relaxation times does not depend on salt content in the PEO system. The relaxation peak for the imaginary part of electric modulus (M″) provides information on long-range motion of dipoles. Summarizing the results from imaginary part of impedance spectrum (Z″), tan δ (imaginary/real of permittivities) and M″ for the two systems under the discussion, PEO behaves like a mixture of chains with dipoles. There are interactions between the dipoles, but they are relaxing individually. Therefore, we see PEO-salt system as a polymer electrolyte where only a tiny fraction of added salt molecules becomes electrically active in promoting conductance. However, ENR-25-salt system behaves just as a macroscopic dipole and it can not display electrode polarization or electric relaxation because there is no mobility of individual dipoles. Hence, ENR-25-salt does not form a polymer electrolyte in the classic sense.

Room-Temperature Skyrmions in an Antiferromagnet-Based Heterostructure.

Magnetic skyrmions as swirling spin textures with a nontrivial topology have potential applications as magnetic memory and storage devices. Since the initial discovery of skyrmions in non-centrosymmetric B20 materials, the recent effort has focused on exploring room-temperature skyrmions in heavy metal and ferromagnetic heterostructures, a material platform compatible with existing spintronic manufacturing technology. Here, we report the surprising observation that a room-temperature skyrmion phase can be stabilized in an entirely different class of systems based on antiferromagnetic (AFM) metal and ferromagnetic (FM) metal IrMn/CoFeB heterostructures. There are a number of distinct advantages of exploring skyrmions in such heterostructures including zero-field stabilization, tunable antiferromagnetic order, and sizable spin-orbit torque (SOT) for energy-efficient current manipulation. Through direct spatial imaging of individual skyrmions, quantitative evaluation of the interfacial Dzyaloshinskii-Moriya interaction, and demonstration of current-driven skyrmion motion, our findings firmly establish the AFM/FM heterostructures as a promising material platform for exploring skyrmion physics and device applications.

Confidence in data recorded with land seismic recorders

Seismic contractors and their clients constantly strive to increase the productivity of land seismic acquisition projects, and this combined with a trend for denser receiver geometries is resulting in much larger volumes of data being acquired on a daily basis. This has created a challenge for the checking of data consistency and its suitability for imaging, and has led to new approaches to in-field quality control. In addition, land seismic recording equipment has been evolving, creating divergences in the way that different systems operate, and three categories of land systems have emerged that can be separately identified – cabled systems, wireless systems, and cross-technology systems. These different classes of systems have distinctive approaches to in-field quality control capabilities, associated with their philosophy and architecture – QC may be acquired in real time, it may be collected from the equipment in-field with some field crew effort, or indeed there may be no QC acquired at all. Some equipment manufacturers insist that with the greatly improved reliability of modern electronics, monitoring of QC during seismic acquisition is no longer of importance. However, for most seismic contractors and the great majority of their clients the reassurance provided by QC monitoring is an important aspect of the operations. In this paper, we firstly discuss how land recorders have evolved and the impact of QC, then describe the different categories of land systems focusing principally on their QC capabilities, and finally discuss the operations of QC during acquisition projects.

Identification of Curie temperature distributions in magnetic particulate systems

This paper develops a methodology for extracting the Curie temperature distribution from magnetisation versus temperature measurements which are realizable by standard laboratory magnetometry. The method is integral in nature, robust against various sources of measurement noise, and can be adopted to a wide range of granular magnetic materials and magnetic particle systems. The validity and practicality of the method is demonstrated using large-scale Monte–Carlo simulations of an Ising-like model as a proof of concept, and general conclusions are drawn about its applicability to different classes of systems and experimental conditions.

An LMI-Based H∞ Discrete-Time Nonlinear State Observer Design for an Anaerobic Digestion Model

This paper is devoted to the design of an H∞ discrete-time nonlinear state observer for an anaerobic digestion model. Indeed, the designed observer can be used for different class of systems, mainly linear systems, LPV systems with known and bounded parameters, and nonlinear Lipschitz systems. We use an LMI approach to guarantee the H∞ asymptotic stability of the estimation error despite the disturbances affecting the system dynamics and measurements. The synthesised LMI is relaxed due to the inclusion of additional decision variables which enhance its feasibility. This was possible due to the use of a suitable reformulation of the Young’s inequality. Simulation results are given to show the robustness of the designed observer.

Experimental soft-matter science

Soft condensed matter refers to materials where the constituent building blocks are larger than atoms but smaller than the system itself. The large size of the constituent particles makes these soft materials distinctive from hard condensed matter systems. Soft matter is easily deformable, dissipative, disordered, nonlinear, far from equilibrium, thermal and entropic, slow, observable, susceptible to external fields, patterned, nonlocal, interfacial elastic, memory retaining, and active. This article surveys soft-matter science and discusses different classes of systems including colloids; emulsions; foams; glassy, granular, and jammed matter; liquid crystals; polymers; adaptive mechanical metamaterials; and active matter.

Research on the Poincar\xe9 center-focus problem of some cubic differential systems by using a new method

In this article, we discuss the Poincaré center-focus problem of some cubic differential systems by using a new method (Mironenko’s method) and obtain some new sufficient conditions for a critical point to be a center. By using this method we not only solve a center-focus problem, but also at the same time, we open a class of differential systems, which do not have to be polynomial differential systems, with the same qualitative behavior at the critical point.

OPPORTUNITIES OF ELECTRO-OPTIC VISUALIZATION PRACTICAL APPLICATIONS ON BOARD THE AIRCRAFT

The article covers the following issues: the development and practical application of airborne electro-optic systems in the civil aviation aircraft. They provide flight visual information for the pilot day and night in visual and instrument weather conditions. The legal documents establishing the requirements for the application of this type of electro-optic systems in aircraft are presented. The classification of airborne electro-optic systems, commonly named as electronic visualization systems is analyzed. The ways of implementing the recommendations in their construction are considered. There have been analyzed the possibilities of systems of different classes: enhanced vision systems (EVS), synthetic vision systems (SVS), combine vision systems (CVS) and on-board vision systems with advanced visualization features, Enhanced Flight Vision Systems (EFVS). It is determined that nowadays EVS systems are considered to be the potential application systems. In order to analyze the possibilities of practical application of such systems in the issues of flight safety at low altitude and landing, flight experiments of the system installed on a light helicopter were conducted. The research introduces the results of flight experiments on the practical work of television and infrared (IR) viewing channels of a promising typical system in simple and complex observation conditions. Based on the results of flight experiments, a conclusion can be made about the relevance of practical application of electronic visualization systems on board the aircraft to ensure flight safety. It is determined that the systems can be used in flight both for land observation tasks and ensuring a safe flight. When flying the helicopter at low altitude and landing procedures the pilot should use visual information from the rear hemisphere of the lower tail unit by electro-optical visualization system. It was elicited that in the infrared (IR) channel and the fast rotation of visualization system camera located there is a corresponding delay of vision direction and the actual direction of flight. The vision is blurred. In the mode of the infrared spectrum information there appears a filtering problem of interference caused by helicopter engine exhaust gases and snow in the sector of observation. It makes it more difficult to obtain the benefits of visualization systems vision in adverse weather conditions. The conclusions indicated that perspective visualization systems for IR channels require additional use of methods and algorithms to ensure high-definition vision.

RATING MODELS AND INFORMATION TECHNOLOGIES APPLICATION FOR MANAGEMENT OF ADMINISTRATIVE-TERRITORIAL COMPLEXES

Purpose. The paper aims to develop rating models and related information technologies designed to resolve the tasks of strategic planning of the administrative and territorial units’ development, as well as the tasks of multi-criteria control of inhomogeneous multiparameter objects operation. Methodology. When solving problems of strategic planning of administrative and territorial development and heterogeneous classes management of objects under control, a set of agreed methods is used. Namely the multi-criteria properties analysis for objects of planning and management, diagnostics of the state parameters, forecasting and management of complex systems of different classes. Their states are estimated by sets of different quality indicators, as well as represented by the individual models of operation process. A new information technology is proposed and created to implement the strategic planning and management tasks. This technology uses the procedures for solving typical tasks, that are implemented in MS SQL Server. Findings. A new approach to develop models of analyze and management of complex systems classes based on the ratings has been proposed. Rating models development for analysis of multicriteria and multiparameter systems has been obtained. The management of these systems is performed on the base of parameters of the current and predicted state by non-uniform distribution of resources. The procedure of sensitivity analysis of the changes in the rating model of inhomogeneous distribution of resources parameters has been developed. The information technology of strategic planning and management of heterogeneous classes of objects based on the rating model has been created. Originality. This article proposes a new approach of the rating indicators’ using as a general model for strategic planning of the development and management of heterogeneous objects that can be characterized by the sets of parameters measured on different scales. At this the control of separate elements is realized by the way of individual mental models construction and application of functioning processes. The procedure for evaluating of the prediction reliability based on multivariate linear extrapolation method was proposed. Practical value. The proposed method of strategic planning of the complex systems’ development based on rating models and developed information technology are representing the complex of automated tools to ensure effective economical and technological control of non-uniform sets of multiparameter objects. The new solutions of typical tasks of strategic planning and development of complex objects management procedure are implemented in the information technology of rating estimation (rating definition, sensitivity analysis, clustering, diagnostics, forecasting, resource allocation, multi-criteria analysis etc.). Application of the proposed information technology can automate the task of analysis and strategic planning of the administrative-territorial complexes. The technology can be used for monitoring, analysis, strategic planning and management of several complex system types simultaneously.

Clustering of exceptional points and dynamical phase transitions

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The eigenfunctions are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wavefunctions. At and near an EP, the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. When the parameters are tuned to the point of maximum width bifurcation, the phase rigidity suddenly increases up to its maximum value. This means that the eigenfunctions become almost orthogonal at this point. This unexpected result is very robust as shown by numerical results for different classes of systems. Physically, it causes an irreversible stabilization of the system by creating local structures that can be described well by a Hermitian Hamilton operator. Interesting non-trivial features of open quantum systems appear in the parameter range in which a clustering of EPs causes a dynamical phase transition.

Ferric Uptake Regulator Fur Control of Putative Iron Acquisition Systems in Clostridium difficile.

Clostridium difficile is an anaerobic, Gram-positive, spore-forming opportunistic pathogen and is the most common cause of hospital-acquired infectious diarrhea. Although iron acquisition in the host is a key to survival of bacterial pathogens, high levels of intracellular iron can increase oxidative damage. Therefore, expression of iron acquisition mechanisms is tightly controlled by transcriptional regulators. We identified a C. difficile homologue of the master bacterial iron regulator Fur. Using targetron mutagenesis, we generated a fur insertion mutant of C. difficile. To identify the genes regulated by Fur in C. difficile, we used microarray analysis to compare transcriptional differences between the fur mutant and the wild type when grown in high-iron medium. The fur mutant had increased expression of greater than 70 transcriptional units. Using quantitative reverse transcriptase PCR (qRT-PCR), we analyzed several of the Fur-regulated genes identified by the microarray and verified that they are both iron and Fur regulated in C. difficile. Among those Fur- and iron-repressed genes were C. difficile genes encoding 7 putative cation transport systems of different classes. We found that Fur was able to bind the DNA upstream of three Fur-repressed genes in electrophoretic mobility shift assays. We also demonstrate that expression of Fur-regulated putative iron acquisition systems was increased during C. difficile infection using the hamster model. Our data suggest that C. difficile expresses multiple iron transport mechanisms in response iron depletion in vitro and in vivo. Clostridium difficile is the most common cause of hospital-acquired infectious diarrhea and has been recently classified as an "urgent" antibiotic resistance threat by the CDC. To survive and cause disease, most bacterial pathogens must acquire the essential enzymatic cofactor iron. While import of adequate iron is essential for most bacterial growth, excess intracellular iron can lead to extensive oxidative damage. Thus, bacteria must regulate iron import to maintain iron homeostasis. We demonstrate here that C. difficile regulates expression of several putative iron acquisition systems using the transcriptional regulator Fur. These import mechanisms are induced under iron-limiting conditions in vitro and during C. difficile infection of the host. This suggests that during a C. difficile infection, iron availability is limited in vivo.

On a connection between a class of [formula omitted]-deformed algebras and the Hausdorff derivative in a medium with fractal metric

Over the recent decades, diverse formalisms have emerged that are adopted to approach complex systems. Amongst those, we may quote the q-calculus in Tsallis’ version of Non-Extensive Statistics with its undeniable success whenever applied to a wide class of different systems; Kaniadakis’ approach, based on the compatibility between relativity and thermodynamics; Fractional Calculus (FC), that deals with the dynamics of anomalous transport and other natural phenomena, and also some local versions of FC that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations.The question we might ask is whether or not there are common aspects that connect these alternative approaches. In this short communication, we discuss a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, Tsallis’ framework and Kaniadakis’ scenario, with local form of fractional-derivative operators defined in fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. This connection opens up new perspectives for theories that satisfactorily describe the dynamics for the transport in media with fractal metrics, such as porous or granular media. Possible connections with other alternative definitions of FC are also contemplated. Insights on complexity connected to concepts like coarse-grained space–time and physics in general are pointed out.

Existence of homoclinic solutions for a class of difference systems involving p-Laplacian

By using the critical point theory, some existence criteria are established which guarantee that the difference p-Laplacian systems of the form have at least one or infinitely many homoclinic solutions, where , , , , , and are not periodic in n. MSC:34C37, 35A15, 37J45, 47J30.

Weierstrass integrability for a class of differential systems

We characterize the differential equations of the formwhere aj(x) are meromorphic functions in the variable x for j = 0,…,n that admits either a Weierstrass first integral or a Weierstrass inverse integrating factor.