Five-dimensional System Research Articles

Experimental observation of quantum contextuality beyond Bell nonlocality

Bell nonlocality and quantum contextuality are two important resources which, however, behave very differently in many tasks where the quantum correlation has an edge over its classical counterpart. In this work, we directly compare these two behaviors, which via the Cabello-Severini-Winter graph-theoretical approach, can be associated with a same exclusivity graph. In particular, we consider the exclusivity graph that leads to ${I}_{3322}$-type inequalities in the Bell and the contextual scenarios, respectively. We find that maximal violation of Bell inequality is around 6.251, and maximal violation of the noncontextuality inequality is around 6.588 for a five-dimensional system and 6.571 for a four-dimensional system, respectively. The results predict a gap of $\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}0.32$ between quantum contextuality and Bell nonlocality. We then present an experimental observation of the gap by employing both the maximally entangled photon pairs from the spontaneous parametric down-conversion process and the single photons encoded into qudits from an intrinsic defect in gallium nitride. Our results will further deepen the understanding of different types of quantum correlations.

Explicit investment setting in a Kaldor macroeconomic model with macro shock

As the inevitable attributes of macro shocks on macroeconomic system, in this paper, we develop a Kaldor macroeconomic model with shock. The shock is due to the investment uncertainty. We then provide an approach for macroeconomic control by calibrating the evolvement of the shocked Kaldor macroeconomic model with some expected benchmark process. The calibration is realized through the setting for investment. The benchmark process is usually the reflection of decisions or policies. An optimal investment setting associated with a five-dimensional nonlinear system of ordinary differential equations is presented. Through a logical modification for the boundary conditions, the nonlinear system is simplified to be linear and a completely explicit formula for the optimal investment setting is achieved. The rationality of the modification is supported by some stability condition. To cope with the systematic risk caused by the macro shock, we define a dynamic Value-at-Risk(VaR) as the risk measure capturing the risk level of the shocked Kaldor macroeconomic model and introduce a risk constraint into the programming of calibration. Then a constrained investment setting is presented. Finally, we carry out an application of the theoretical results by calibrating the evolvement of the shocked Kaldor macroeconomic model with the business cycle generated from the classical Kaldor model through the investment setting.

Optimal Control Problem of a Non-integer Order Waterborne Pathogen Model in Case of Environmental Stressors

In this work, we extend a mathematical model, which has been proposed for susceptible and infected compartments together with pathogen population, by including recovered subgroup. It is known that environmental pollution, such as contaminated drinking water and lack of an ordinary toilet, affects individuals and such negative impacts can be defined as stressors. In order to include the influence of such stressors, susceptible subpopulation has been divided into two groups as the one affected by stress or not. Thus, spread of the disease is expressed in terms of a five-dimensional system. Moreover, we extend this model with the use of a time fractional derivative due to non-local effects of water pollution and we prove that the solution is non-negative and bounded from above. Then, we perform stability analysis for the disease-free equilibrium point. Afterward, the next step is to apply optimal control theory to optimize the decay rate of pathogens and the stress related parameters so that the number of infected individuals and the pathogen population can be minimized. Finally, we present some numerical results to find out the most appropriate control policy and the effect of the fractional order.

Hidden Hyperchaotic Attractors in a New 5D System Based on Chaotic System with Two Stable Node-Foci

This paper reports some hidden hyperchaotic attractors and complex dynamics in a new five-dimensional (5D) system with only two nonlinear terms. The system is generated by adding two linear controllers to an unusual 3D autonomous quadratic chaotic system with two stable node-foci. In particular, the hyperchaotic system without equilibrium or with only one stable equilibrium can generate two kinds of hidden hyperchaotic attractors with three positive Lyapunov exponents. Numerical methods not only verify the existence of such attractors and hyperchaotic attractors, but also show the dynamical evolution of this system. The 5D system has self-excited attractors and two types of hidden attractors with the change of its parameter. The parameter switching algorithm is further utilized to numerically approximate the attractor. Specifically, the hidden hyperchaotic attractor can be approximated by switching between two self-excited chaotic attractors. Finally, the circuit realization results are consistent with the numerical results.

Hyperchaos and multistability in the model of two interacting microbubble contrast agents.

We study nonlinear dynamics of two coupled contrast agents that are micrometer size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising applications like targeted drug delivery and noninvasive therapy. Here, we consider a model of two such bubbles interacting via the Bjerknes force and exposed to an external ultrasound field. We demonstrate that in this five-dimensional nonlinear dynamical system, various types of complex dynamics can occur, namely, we observe periodic, quasiperiodic, chaotic, and hypechaotic oscillations of bubbles. We study the bifurcation scenarios leading to the onset of both chaotic and hyperchaotic oscillations. We show that chaotic attractors in the considered system can appear via either the Feigenbaum cascade of period-doubling bifurcations or the Afraimovich-Shilnikov scenario of torus destruction. For the onset of hyperchaotic dynamics, we propose a new bifurcation scenario, which is based on the appearance of a homoclinic chaotic attractor containing a saddle-focus periodic orbit with its two-dimensional unstable manifold. Finally, we demonstrate that the dynamics of two bubbles can be essentially multistable, i.e., various combinations of the coexistence of the above mentioned attractors are possible in this model. These cases include the coexistence of a hyperchaotic regime with an attractor of any other remaining type. Thus, the model of two coupled gas bubbles provides a new example of physically relevant system with multistable hyperchaos.

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

In this paper, I propose a fractional-order mathematical five-dimensional dynamical system modeling a SVEIR model of infectious disease transmission in a chemostat. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if R > 1, then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable in R 5. Finally, some numerical tests are done using the ”PECE” method in order to validate the obtained results.

The Spread of A-H1N1 Swine Flu with Prevention and Healing Efforts in a Mixed Population: Mathematical Model and Dynamical Analysis

Influenza is a respiratory tract infection caused by a virus. Infection of A-H1N1 influenza virus can cause outbreaks in all countries in the world. The outbreak of A-H1N1 influenza virus occurred in Indonesia in April 2009. This paper develops a mathematical model of the spread of A-H1N1 influenza with prevention and healing efforts for humans in mixed populations. This model is a five-dimensional system of nonlinear differential equations that shows the effect of vaccination and treatment on the spread of A-H1N1 influenza disease. Dynamic simulation provides information about the final results of the condition of the spread of influenza disease in various cases. The sensitivity analysis can be done in two ways, namely by using the sensitivity index of a parameter to a particular variable or by using a graph method.

Health-related quality of life in systemic sclerosis compared with other rheumatic diseases: a cross-sectional study

BackgroundSystemic sclerosis (SSc) is a rare autoimmune disease characterized by fibrosis of the skin and the involvement of multiple internal organs. Previous studies reported poorer health-related quality of life (HRQoL) in patients with SSc compared with the general population. However, very little is known about how HRQoL in SSc patients compares with that in patients with other systemic autoimmune diseases, such as rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), and Sjogren’s syndrome (SjS). Thus, the main aim of this study was to compare HRQoL in SSc patients, patients with other rheumatic diseases, and the general population.MethodsIn this cross-sectional study, patients from the rheumatology clinics of Seoul National University Hospital with SSc, RA, SLE, and SjS were enrolled via a random sampling technique. HRQoL was captured by the Short Form (36) health survey (SF-36), the Short Form Six-Dimensional health index (SF-6D), and the EuroQol Five-Dimensional descriptive system (EQ-5D). Demographic characteristics and standardized disease activity for each disease were also obtained. Previously reported data from 600 healthy Koreans were used for the healthy controls. An ANCOVA test was used to compare the SF-36, SF-6D, and EQ-5D values between study subjects with adjustments for age, sex, disease duration, comorbidities, and disease activity status.ResultsOne hundred twenty patients were included in each of the SSc, RA, SLE, and SjS cohorts. Patients with rheumatic diseases had significantly lower SF-36, SF-6D, and EQ-5D scores than healthy controls (all P < 0.001). After statistical adjustments, SSc patients reported significantly lower mental component summary (MCS) scores than patients with RA (P < 0.001) or SLE (P = 0.001). Specifically, the mental health and general health domains were significantly lower in SSc patients than reported in RA or SLE patients (P < 0.001 and P = 0.001, respectively, in both domains). In SSc patients, higher modified Rodnan skin scores (mRSS) correlated with lower MCS scores.ConclusionsSSc patients report poorer HRQoL than patients with RA or SLE. The extent of skin involvement is associated with poorer HRQoL in SSc patients.Trial registrationNCT03257878. Registered 22 August 2017

A new five-dimensional four-wing hyperchaotic system with hidden attractor, its electronic circuit realisation and synchronisation via integral sliding mode control

This paper reports a new five-dimensional four-wing hyperchaotic system with hidden attractor. First, this paper discusses the dynamic properties of the new four-wing system with a detailed bifurcation analysis, coexistence of attractors and multistability, offset boosting, Lyapunov exponents, etc. It is shown that the new four-wing system has no rest point and thus it exhibits hidden attractor. The new four-wing system exhibits two positive Lyapunov characteristic exponents and a large value of Kaplan-Yorke dimension indicating high complexity of the system. We realise the dynamic equations of the new four-wing system with an electronic circuit and simulations via MultiSIM. As a control application, we derive new results for the complete synchronisation of the new four-wing system via integral sliding mode control. MATLAB simulations are adequately provided to illustrate modelling and applications of the new four-wing system with hyperchaotic four-wing attractor.

A new five-dimensional four-wing hyperchaotic system with hidden attractor, its electronic circuit realisation and synchronisation via integral sliding mode control

This paper reports a new five-dimensional four-wing hyperchaotic system with hidden attractor. First, this paper discusses the dynamic properties of the new four-wing system with a detailed bifurcation analysis, coexistence of attractors and multistability, offset boosting, Lyapunov exponents, etc. It is shown that the new four-wing system has no rest point and thus it exhibits hidden attractor. The new four-wing system exhibits two positive Lyapunov characteristic exponents and a large value of Kaplan-Yorke dimension indicating high complexity of the system. We realise the dynamic equations of the new four-wing system with an electronic circuit and simulations via MultiSIM. As a control application, we derive new results for the complete synchronisation of the new four-wing system via integral sliding mode control. MATLAB simulations are adequately provided to illustrate modelling and applications of the new four-wing system with hyperchaotic four-wing attractor.

FORMATION OF THE SYSTEM OF SUSTAINABLE USE OF WATER RESOURCES IN INDUSTRIAL COMPLEX

The triad of value-oriented dominants of development, formation, and practical implementation into the economy, as well as further development in the resource limitations of the five-dimensional spatial system of natural resources assets management system in Ukraine were defined and described. They were disclosed according to three areas of generation of multi-component capacities for rationalization of spatial management, which are delineated according to constitutive and key properties of management of the natural and economic space of the state, its regions, and separate territories. Grouping and delineation were carried out in the directions which: are caused by the structure and target and specific functions of the system; form the capacity of a complex system for self-preservation; characterize the behavioural tactic and strategy of a spatial system for achievement of the objective and resolving the target tasks in the field of rationalization of the state’s natural resources assets management. A set of model solutions was worked out and justified for calculation of the basic indices of its operation, namely: the relative organization of the spatial system architecture, structural and functional organization of its parameters, degree of uncertainty of the condition of a multi-dimensional management system, reliability of its operation as capacities for failure-free operation in various conditions of functioning, capacity of the spatial system and its five subsystems for self-preservation. It was proved and confirmed that building up a new format of a spatial system of natural resources assets management with simultaneous incorporation of the provisions of the systemic, synergetic, structural and informational, and platform theoretical approaches protects rationalization of development and usage of the existing strategic potential of Ukraine and its regions based on the consequences of achievement of sustainable economy with resource limitations, accompanied with constant growth of socio-political threats and risks.

SYSTEM-ORGANIZED COMBINATION OF VALUE-ORIENTED DOMINANT FORMATION OF NATURAL AND ECONOMIC SPACE

The triad of value-oriented dominants of development, formation, and practical implementation into the economy, as well as further development in the resource limitations of the five-dimensional spatial system of natural resources assets management system in Ukraine were defined and described. They were disclosed according to three areas of generation of multi-component capacities for rationalization of spatial management, which are delineated according to constitutive and key properties of management of the natural and economic space of the state, its regions, and separate territories. Grouping and delineation were carried out in the directions which: are caused by the structure and target and specific functions of the system; form the capacity of a complex system for self-preservation; characterize the behavioural tactic and strategy of a spatial system for achievement of the objective and resolving the target tasks in the field of rationalization of the state’s natural resources assets management. A set of model solutions was worked out and justified for calculation of the basic indices of its operation, namely: the relative organization of the spatial system architecture, structural and functional organization of its parameters, degree of uncertainty of the condition of a multi-dimensional management system, reliability of its operation as capacities for failure-free operation in various conditions of functioning, capacity of the spatial system and its five subsystems for self-preservation. It was proved and confirmed that building up a new format of a spatial system of natural resources assets management with simultaneous incorporation of the provisions of the systemic, synergetic, structural and informational, and platform theoretical approaches protects rationalization of development and usage of the existing strategic potential of Ukraine and its regions based on the consequences of achievement of sustainable economy with resource limitations, accompanied with constant growth of socio-political threats and risks.

The Spatial-Temporal Characteristics and Dilemmas of Sustainable Urbanization in China: A New Perspective Based on the Concept of Five-in-One

A large amount of ink has been spilled to paint the picture of China’s urbanization. However, more research might be done on the connotation of sustainable urbanization in China. On the basis of a literature review, this study is the first to propose the perspective of evaluating the sustainability of urbanization from the five dimensions of urbanization: economic, political, cultural, social, and ecological. Based on the Analytic Hierarchy Process (AHP) method and entropy method, a five-dimensional indicator system was established to evaluate the urbanization quality of 31 provincial regions in China during 2005–2015. Then, the coupling coordination degree model was used to calculate the coupling coordination degree of the five dimensions for each region. Furthermore, Moran’s I index and a local indicators of spatial association (LISA) cluster map were used to measure and describe the spatial disparity. Finally, a factor identification model was used to recognize the weaknesses of each region. This study leads to four major findings. (1) In 2015, only ecological urbanization had a high-quality and balanced development, while the development of cultural urbanization was inadequate and regionally unbalanced. Economic, ecological, and cultural dimensions had a significantly positive global spatial autocorrelation. The local spatial autocorrelation varies with dimension. (2) The quality of comprehensive urbanization increased during 2005–2015, while the regional disparity experienced a reduction. A positive global spatial autocorrelation was shown during 2005–2015. The High-High type in the eastern coastal areas centralized over time, while the Low-Low type in the western areas experienced a decline, and the Low-High type was stabilized in the central areas. Only Chongqing was in the High-Low type in 2015. (3) The increase of coupling coordination degree and decrease of coefficient of variation indicated a favorable situation. The coupling coordination degree also had a positive global spatial autocorrelation during 2005–2015. Both the High-High and Low-Low types experienced an obvious shrink and displacement. The Low-High type expanded and centralized in the central areas, while the High–Low type was in Guangdong in 2005, and in Chongqing in 2015. (4) The highest obstacle degrees of each region were all within the cultural dimension, while the ecological dimension caused the least resistance. The lack of innovation had become the biggest barrier in most regions. Based on the above conclusions, this paper concludes with recommendations for policy makers to advance sustainable urbanization in China. Meanwhile, this study can provide lessons and suggestions for other developing countries in the world.

Stability analysis of a Bose–Einstein condensate trapped in a generic potential

We investigate the dynamical behavior of the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A five-dimensional dynamical system is found (due the symmetry of the Gross-Pitaevskii equation interacting with a potential), where the Thomas-Fermi approximation constrains the parameter space of solutions. We show that for values of the power law exponent equal or smaller than 2 the system seems to be stable. However, when the corresponding exponent is bigger than 2, the instability of the system grows when the power law exponent grows, indicating that large values of the aforementioned parameter can be related to a loss in the number of particles from the condensed state. This fact can be used also to show that the stability conditions of the condensate are highly sensitive to the exponent associated with the external potential.

Nonlinear thermoacoustic mode synchronization in annular combustors

Nonlinear coupling between azimuthal and axisymmetric modes in annular combustors is studied analytically. Based on the thermoacoustic wave equation, a model featuring three nonlinearly coupled oscillators is derived. Two oscillators represent the dynamics of an azimuthal mode, and the third accounts for the axisymmetric mode. A slow-time system for the evolution of the mode amplitudes and phases is obtained through the application of the method of averaging. The averaged system is shown to accurately reproduce the solutions of the full oscillator model. Analysis of this five-dimensional dynamical system shows that a standing azimuthal mode may synchronize with an axisymmetric mode, provided that their individual resonance frequencies and growth rates are similar. This phase-coupled two-mode oscillation corresponds to the so-called slanted mode, observed in recent experiments involving an annular model combustion chamber. Quantitative conditions for the occurrence of mode synchronization are derived in terms of the growth rate ratio and a frequency detuning parameter. The analysis results are found to be consistent with experimental observations of the slanted mode.

Quality of life and reconstructive surgery efforts in severe hand injuries.

Introduction:Severe hand trauma, leading to extensive skeletal and tissue defects, requires plastic surgical reconstruction of the highest level aiming at maximizing function and aesthetics. The intention of this study was to investigate clinical parameters and resource consumption connected with severe hand injuries, with specific emphasis on a follow-up evaluation of quality of life after the reconstruction process.Materials and methods:In this retrospective study, we evaluated patients with severe hand injuries from 2013 to 2016 who had completed surgical and non-surgical treatment. Measures included total period of therapy (TPT) in days, total duration of operations including anesthesia (TOA), total duration of all operations (TO), and total number of operations (TNO). We also determined total inpatient stay (TIS), total number of clinic presentations with interventions (TNPI), initial hand injury severity score (iHISS), and inpatient proceeds (IPP) in Euros (€). Correlation was assessed between iHISS and TOA, TNO, and TIS. Finally, these patients were reexamined in a follow-up inquiry and the life quality was assessed with the five-level version of the EuroQol five-dimensional (EQ-5D) descriptive system (EQ-5D-5L).Results:We analyzed 12 patients with an average age of 44 years (min. 24 years, max. 75 years). Patients receiving reconstructive surgery experienced median (n{rm{tilde x}}n) TPT of 175 days [interquartile range (IQR), 51–499], TOA of 13 h (IQR, 6–37), TO of 9 h (IQR, 4–25), and TNO of 5 (IQR, 3–11). Further, the patients’ median TIS was 22 days (IQR, 9–86), TNPI was 4 (IQR, 2–8), and iHISS was 77 (IQR, 44–162). The median IPP was 14.595 € (IQR, 5.541–33.709 €). IHISS was positively correlated with Pearson’s r for TIS (0.817), TOA (0.857), and TNO (0.871). The EQ-5D-5L index value resulted in a high level of life quality with a median of 0.898 (min. 0.8, max. 1).Conclusion:Severe hand injuries are related to high efforts for surgical and functional reconstructions, which result in high quality of life measured with the EQ-5D-5L assessment. However, for a defined collective of patients, myoelectric prosthetic functional replacement should be considered. Further studies are necessary to examine functional outcomes and quality of life after bionic prosthetic replacement. Also, a bionic reconstruction score to define hard criteria for taking an acute treatment decision is necessary.

A Novel Hyperchaotic Image Encryption Scheme Based on DNA Encoding, Pixel-Level Scrambling and Bit-Level Scrambling

In this paper, a novel image encryption scheme has been proposed using pixel-level scrambling, bit-level scrambling, and DNA encoding. First, initial conditions of five-dimensional hyperchaotic system are computed and chaotic sequences are generated. Then, pixel-level scrambling and bit-level scrambling are implemented to permute the plain image. Permuted image and generated pseudorandom sequence are executed decomposition operations in order to enhance security. DNA encoding, DNA xor operation, and DNA complementary rules are also adopted to improve the security of the cryptosystem. Experiments results and theoretical analysis show that the proposed scheme is secure enough and can resist known plain text attack, statistical attacks, and differential attacks. It is suitable for practical application.

A new hidden chaotic attractor with extreme multi-stability

The topic of hidden attractors is a very hot topic in nonlinear dynamics. Multi-stability is another important topic in that area. One recent important category of multi-stable systems is “systems with extreme multi-stability”. In this paper we introduce a new five-dimensional chaotic system with both hidden attractors and extreme multi-stability. Such systems are very rare in literature. Also, we show its feasibility by the help of electronic circuit implementation.

Inventory growth cycles with debt-financed investment

We propose a continuous-time stock-flow consistent model for inventory dynamics in an economy with firms, banks, and households. On the supply side, firms decide on production based on adaptive expectations for sales demand and a desired level of inventories. On the demand side, investment is determined as a function of utilization and profitability and can be financed by debt, whereas consumption is independently determined as a function of income and wealth. Prices adjust sluggishly to both changes in labour costs and inventory. Disequilibrium between expected sales and demand is absorbed by unplanned changes in inventory. This results in a five-dimensional dynamical system for wage share, employment rate, private debt ratio, expected sales, and capacity utilization. We analyze two limiting cases: the long-run dynamics provides a version of the Keen model with effective demand and varying inventories, whereas the short-run dynamics gives rise to behaviour that we interpret as Kitchin cycles.

Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points

Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five‐dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.