Assessing sigmoidal function on memristive maps.

Memristors offer a crucial element for constructing discrete maps that have garnered significant attention in complex dynamics and various potential applications. In this study, we have integrated memristive and sigmoidal function to propose innovative mapping techniques. Our research confirms that the amalgamation of memristor and sigmoidal functions represents a promising approach for creating both 2D and 3D maps. Particularly noteworthy are the chaotic maps featuring multiple sigmoidal functions and multiple memristors, as highlighted in our findings. Specifically focusing on the novel STMM1 map, we delve into its dynamics and assess its feasibility. Intriguingly, the introduction of sigmoidal functions leads to alterations in the quantity of fixed points and the symmetry of the map.

A dissipative and entropy-optimized MHD nanomaterial mixed convective flow for engineering applications.

Background and objective: Nanomaterials play significant roles in numerous industrial and engineering applications, like nuclear plants, paper production, thermal power plants, glass fibres, manufacturing of medicines, medical instruments, micro-electronics and polymer sheet extrusion. In view of such important applications, in this study, we discuss the magnetohydrodynamic flow of a nanofluid over an inclined surface by employing the Darcy-Forchheimer model. The Buongiorno model is applied to understand the various important aspects of the nanofluid. Radiation, magnetic field, dissipation and entropy generation in a chemically reactive flow are also discussed. Methodology: The governing nonlinear expressions were transformed into a dimensionless system through adequate transformations. The obtained non-dimensional systems were computed by the NDSolve approach. Results: Physical illustrations for the flow, temperature, concentration and entropy rate via emerging variables were examined. Here an enhancement in velocity was seen for the mixed convection variable, while opposite impacts on flow and temperature were noticed through the Hartman number. A higher Eckert number was obtained with a rise in temperature, while a decrease in concentration was noticed for the thermophoresis variable. An augmentation in the entropy rate was detected for radiation, while the thermal transport rate was boosted by thermophoresis.

Non-similar solution development for entropy optimized flow of Jeffrey liquid.

Mixed convection in dissipative entropy optimized stagnation point flow of nanomaterial towards stretching Riga sheet is addressed. Brownian and thermophoresis diffusions for nanomaterial are accounted. Constitutive relations for Jeffrey material are utilized. Non-similar solutions for the governing differential systems are developed. OHAM is employed for the convergent series solutions development. Outcomes of pertinent variables on flow quantities of interest are graphically organized. Finally the concluding remarks are arranged.

A study on fractional HBV model through singular and non-singular derivatives.

The current study's aim is to evaluate the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers using two different numerical algorithms and various values of the fractional-order parameter. We considered the model with two different fractional-order derivatives, namely the Caputo derivative and Atangana-Baleanu derivative in the Caputo sense (ABC). The considered derivatives are the most widely used fractional operators in modeling. We present some mathematical analysis of the fractional ABC model. The fixed-point theory is used to determine the existence and uniqueness of the solutions to the considered fractional model. For numerical results, we show a generalized Adams-Bashforth-Moulton (ABM) method for Caputo derivative and an Adams type predictor-corrector (PC) algorithm for Atangana-Baleanu derivatives. Finally, the models are numerically solved using computational techniques and obtained results graphically illustrated with a wide range of fractional-order values. We compare the numerical results for Caputo and ABC derivatives graphically. In addition, a new variable-order fractional network of the HBV model is proposed. Considering the fact that most communities interact with each other, and the rate of disease spread is affected by this factor, the proposed network can provide more accurate insight for the modeling of the disease.

A study on fractional COVID-19 disease model by using Hermite wavelets.

The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems.

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy.

This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19.

The discrete fractional duffing system: Chaos, 0-1 test, C0 complexity, entropy, and control.

In this paper, we study the dynamics and control of a Caputo fractional difference form of the Duffing map. We use phase plots, bifurcation diagrams, and Lyapunov exponents to establish the existence of chaos over a wide range of fractional orders and examine the nature of the dynamics. Also, we present the 0-1 test to detect chaos and C0 complexity, which is an alternative nonlinear statistical measure that can quantify the regularity of a time series. In addition, we measure the approximate entropy to see the performance of our numerical results. Through phase plots and bifurcation diagrams, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. A one-dimensional feedback stabilization controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Simulation results have been carried out to illustrate the findings of the study.

Solvability and stability of a fractional dynamical system of the growth of COVID-19 with approximate solution by fractional Chebyshev polynomials.

Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a system of coupled differential equations, which describes the dynamics of the infection spreading between infected and asymptomatic styles. The healthy population properties are measured due to the social meeting. The result is associated with a macroscopic law for the population. This dynamic system is appropriate to describe the performance of growth rate of the infection and to verify if its control is appropriately employed. A unique solution, under self-mapping possessions, is investigated. Approximate solutions are presented by utilizing fractional integral of Chebyshev polynomials. Our methodology is based on the Atangana-Baleanu calculus, which provides various activity results in the simulation. We tested the suggested system by using live data. We found positive action in the graphs.

Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis.

The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the γ̅-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the γ̅-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent γ̅-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.

Development of spreading symmetric two-waves motion for a family of two-mode nonlinear equations.

In this work, a functional operator extracted from Korsunsky's technique is used to produce new two-mode nonlinear equations. These new equations describe the motion of two directional solitary-waves overlapping with an increasing phase-velocity and affected by two factors labeled as the dispersion and nonlinearity coefficients. To investigate the dynamics of this two-mode family, we construct the two-mode KdV-Burgers-Kuramoto equation (TMKBK) and two-mode Hirota-Satsuma model (TMHS). Two efficient schemes are used to assign the necessary constraints for existence of solutions and to extract them. The role of the phase-velocity on the motion of the obtained two-wave solutions is investigated graphically. Finally, all the obtained solutions are categorized according to their physical shapes.

Cattaneo-Christov heat flux (CC model) in mixed convective stagnation point flow towards a Riga plate.

This research article proposes an improved Fourier law of heat conduction (Cattaneo-Christov) in presence of heat source/sink. The heat transport characteristics are modeled for mixed convective stagnation point flow by a Riga plate. Flow is generated due to linear stretching velocity. The partial differential system is changed to ordinary differential system through implementing appropriate transformations. Series solutions are developed through semi-analytical method called as homotopy analysis method. Present research article is related to the improved Fourier law of heat conduction (Cattaneo-Christov) over a linear stretchable surface of Riga plate when fluid saturates porous space. The main outcomes of present communication are summarized as: (i) velocity of material particles decreases subject to larger inverse Darcy-number while it enhances via velocity ratio and magnetic parameters (ii) temperature distribution as well as layer thickness enhance for higher estimations of Eckert number and heat source parameter while it decays against Prandtl number (iii) skin friction coefficient decreases through higher values of inverse Darcy number and mixed convection parameter.

Cattaneo-Christov (CC) heat flux model for nanomaterial stagnation point flow of Oldroyd-B fluid.

Background Magnetohydrodynamic (MHD) stagnation point flow of Oldroyd-B nanoliquid is discussed in presence of Cattaneo-Christov mass and heat fluxes. Impacts of Brownian motion and thermophoresis are discussed. Convergent solution for nonlinear analysis are organized for velocity, temperature and concentration. Method Average residual error is calculated with the help of optimal homotopy analysis method (OHAM). Results Prominent features of interesting parameters on concentration, velocity and temperature are scrutinized. Velocity field has reverse trend for Deborah number against retardation and relaxation times. Temperature and concentration have similar results versus thermophoresis parameter. Conclusions: 1: Velocity has opposite impact for Deborah number for relaxation and retardation time. 2: Velocity boosts up for higher ratio parameter. 3: Velocity against magnetic parameter is decreased. 4: Thermal upsurges versus thermal relaxation time parameter. 5: Outcomes of thermophoretic parameter and Brownian motion parameter on temperature are quantitatively similar. 6: Concentration boosts up via Brownian parameter. 7: Concentration have similar characteristics for both Prandtl number and thermophoretic parameter.

Comparing Bibliometric Analysis Using PubMed, Scopus, and Web of Science Databases.

Literature databases (i.e., PubMed, Scopus, and Web of Science) differ in terms of their coverage, focus, and the tool they provide. PubMed focuses mainly on life sciences and biomedical disciplines, whereas Scopus and Web of Science are multidisciplinary. The protocol described in the current study was used to search for publications from Jordanian authors in the years 2013-2017. In this protocol, how to use each database to conduct this type of search is explained in detail. A Scopus search resulted in the highest number of documents (11,444 documents), followed by a Web of Science search (10,943 documents). PubMed resulted in a smaller number of documents due to its narrower scope and coverage (4,363 documents). The results also show a yearly trend in: (1) the number of publications, (2) the disciplines that have the most publications, (3) the countries of collaboration, and (4) the number of open access publications. In contrast, PubMed has a sophisticated keyword optimization service (i.e., Medical Subject Heading, or MeSH), while both Scopus and Web of Science provide search analysis tools that can produce representative figures. Finally, the features of each database are explained in detail and several indices that can be extracted using the search results are provided. This study provides a base for using literature databases for bibliometric analysis.

Solitary solutions for time-fractional nonlinear dispersive PDEs in the sense of conformable fractional derivative.

In this paper, the time-fractional nonlinear dispersive (TFND) partial differential equations (PDEs) in the sense of conformable fractional derivative (CFD) are proposed and analyzed. Three types of TFND partial differential equations are considered in the sense of CFD, which are the TFND Boussinesq, TFND Klein-Gordon, and TFND B(2, 1, 1) PDEs. Solitary pattern solutions for this class of TFND partial differential equations based on the residual fractional power series method is constructed and discussed. Numerical and graphical results are also provided and conferred quantitatively to clarify the required solutions. The results suggest that the algorithm presented here offers solutions to problems in a rapidly convergent series leading to ideal solutions. Furthermore, the results obtained are like those in previous studies that used other types of fractional derivatives. In addition, the calculations used were much easier and shorter compared with other types of fractional derivatives.

Are university rankings useful to improve research? A systematic review.

INTRODUCTION: Concerns about reproducibility and impact of research urge improvement initiatives. Current university ranking systems evaluate and compare universities on measures of academic and research performance. Although often useful for marketing purposes, the value of ranking systems when examining quality and outcomes is unclear. The purpose of this study was to evaluate usefulness of ranking systems and identify opportunities to support research quality and performance improvement. METHODS: A systematic review of university ranking systems was conducted to investigate research performance and academic quality measures. Eligibility requirements included: inclusion of at least 100 doctoral granting institutions, be currently produced on an ongoing basis and include both global and US universities, publish rank calculation methodology in English and independently calculate ranks. Ranking systems must also include some measures of research outcomes. Indicators were abstracted and contrasted with basic quality improvement requirements. Exploration of aggregation methods, validity of research and academic quality indicators, and suitability for quality improvement within ranking systems were also conducted. RESULTS: A total of 24 ranking systems were identified and 13 eligible ranking systems were evaluated. Six of the 13 rankings are 100% focused on research performance. For those reporting weighting, 76% of the total ranks are attributed to research indicators, with 24% attributed to academic or teaching quality. Seven systems rely on reputation surveys and/or faculty and alumni awards. Rankings influence academic choice yet research performance measures are the most weighted indicators. There are no generally accepted academic quality indicators in ranking systems. DISCUSSION: No single ranking system provides a comprehensive evaluation of research and academic quality. Utilizing a combined approach of the Leiden, Thomson Reuters Most Innovative Universities, and the SCImago ranking systems may provide institutions with a more effective feedback for research improvement. Rankings which extensively rely on subjective reputation and "luxury" indicators, such as award winning faculty or alumni who are high ranking executives, are not well suited for academic or research performance improvement initiatives. Future efforts should better explore measurement of the university research performance through comprehensive and standardized indicators. This paper could serve as a general literature citation when one or more of university ranking systems are used in efforts to improve academic prominence and research performance.

The General Solution of Singular Fractional-Order Linear Time-Invariant Continuous Systems with Regular Pencils.

This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative. The complexity of their entropy lies in defining the complete solution of such systems, which depends on introducing a method of decomposing their dynamic states from their static states. The solution is formulated by converting the singular system of regular pencils into a recursive form using the sequence of transformations, which separates the dynamic variables from the algebraic variables. The main idea of this work is demonstrated via numerical examples.