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A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model's behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider the system of reaction–diffusion–advection equations describing the evolution of the spatial distributions of two populations of predators and two prey populations. This model allows us to consider directed migration, the Holling functional response of the second kind, and the hyperbolic prey growth function. We obtain conditions on the parameters under which cosymmetries exist. As a result, multistability is realized, i.e., the one- and two-parameter families of stationary solutions appear. For a homogeneous environment, we analytically derive explicit formulas for equilibria. With a heterogeneous habitat, we computed distributions of species using the method of lines and the scheme of staggered grids. We present the results of violation of cosymmetry and transformation of the family in the case of invasion of a predator. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of a two dimensional linear PDE with a degenerate diffusion and a drift term. The structure of this equation typically arises in some mathematical mean-field models of neural network, and the investigation of the qualitative properties of this equation is still open, and a challenging question. We prove, via a Doeblin-Harris type method, that the solutions converge exponentially fast to the unique stationary state in a L1-weighted norm. [ABSTRACT FROM AUTHOR]

We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered at-risk is modeled using a strictly decreasing general function, mimicking an influential factor that reduces the flow into the addicted class. The basic reproductive number is computed, which determines the local asymptotically stability of the addicted-free equilibrium. Conditions for a forward-backward bifurcation were established using the basic reproductive number and other threshold quantities. A stochastic version of the model is presented, and some numerical examples are shown. Results showed that the influence of the temporarily reformed individuals is highly sensitive to the initial addicted population. [ABSTRACT FROM AUTHOR]

When estimating design local scour depths at structures where the design flows have short durations, equilibrium scour depths can be too conservative. Attempts to develop methods to accurately estimate scour rates and times to reach near equilibrium scour depths have only been moderately successful. The objective of the work reported here was to develop an improved, but still conservative, mathematical model for estimating local scour depth as a function of time for a known flow event. This model also estimates scour rates and the time required for the scour to reach near equilibrium (80%–90%) depths. When used in conjunction with the recently published equilibrium local scour depth model, Sheppard et al., it can be applied to both simple and complex bridge pier structures. When using the scour rate equations presented here, changes in sediment properties with sediment depth can be included in the analysis. Due to the lack of local scour rate data at large structures subjected to live-bed flow conditions, the proposed methodology is currently limited to clear-water scour conditions. [ABSTRACT FROM AUTHOR]

We study the mathematical model of an abstract society in the form of a complex dynamical system with conflict interaction between its elements. New existence conditions are established for equilibrium (compromise) states (fixed points) in the presence of a permanent influence of the environment. Our main results are obtained for systems with three elements (players). In this case, we give a description of all equilibrium states, study their stability depending on the parameter of external influence, and partially describe the basins of attraction for one-point attractors. Several numerical examples are presented. [ABSTRACT FROM AUTHOR]

The present study aims to consider a mathematical eco-epidemiological model involving two fractional operators. To this end, we provide approximate solutions to these fractional systems through the application of a numerical technique that is based on the rule of product integration. This feature contributes greatly to the efficiency and effectiveness of both methods. We have also presented some theoretical discussions related to the equilibrium points of the system. Further, several numerical simulations are presented in order to illustrate the impact of choosing different parameters on the dynamics of the model. It is demonstrated that the obtained numerical results are completely consistent with the expected theoretical results. Moreover, both techniques can be used to solve other problems in epidemiology and describe other problems in the future. The article's model has never been studied via the employed fractional operators, and this is a distinct point for our work and other existing research. [ABSTRACT FROM AUTHOR]

We study a mathematical model of abstract society with redistribution of the social energy of individuals determined by two factors, namely, by the mutual competition and the presence of external influence. The behavior of the analyzed model is described by relatively simple iterative equations generating a dynamic system with discrete time. Fixed points of the system are determined. For some of these points that are attractors, their pools are partially described. In the general case, we prove the convergence of trajectories to the equilibrium states. In particular, it is shown that the individuals with the highest initial energy are doomed to be defeated if one of weaker individuals receives a sufficiently strong external support. Four examples are discussed to illustrate the most interesting cases of external influence on the dynamics of competition between individuals in an abstract society. [ABSTRACT FROM AUTHOR]

The present work describes the development of a mathematical model for the evaluation of the equilibrium scour depth around a single cylindrical pier under the influence of co-existing waves and current. The presented equation includes the effect of the Keulegan–Carpenter number and Froude number on the formation of scour hole. The principle of energy balance is used to form a nonlinear equation of scour, where the energy of incoming flow when collided with the pier is equated with the weight of the sediments moving away from the vicinity of the pier to establish an equilibrium scour depth. An effort has been made to capture the nature of the flow along x-, y-, and z-directions when the current is inclined at an angle θ with the direction of progress of the wave. Further, the scour profile chosen can incorporate any shape and size of the scour hole. The model has been tested against published experimental data pertaining to two cases, namely when the waves are following the current and when the waves are traveling normal to the current. Here, only linear wave is considered while deriving the equation. [ABSTRACT FROM AUTHOR]

This paper analyses the available mathematical models of flight simulators based on the Stewart platform. It was found that there is no model that describes the conditions for stable dynamic equilibrium operation of the Stewart platform as a function of a number of important motion parameters. In this context, a new physical model is proposed based on classical models of theoretical mechanics using the d’Alembert formalism, the concept of stable equilibrium of a mechanical system. This model mathematically separates the stable equilibrium of the flight simulator motion system from the general uniformly accelerated motion. The systems of equations obtained in the framework of the model connect the physical and geometrical parameters of the Stewart platform and make it possible to determine the reactions in the upper hinges of the platform support, the limit values of the position angles in the space of the base of the support of the Stewart platform, under which the condition of stable equilibrium operation of the Stewart platform is satisfied. The proposed physical model and the analytical relations obtained on its basis are of great practical importance: the operator controlling the operation of the Stewart platform-based flight simulator can control the range of parameters during training so as not to bring the flight simulator out of stable equilibrium. [ABSTRACT FROM AUTHOR]

This research paper proposes a hybrid Whale Optimization Algorithm (WOA) variant based on Equilibrium Optimizer (EO), named Equilibrium Whale Optimization Algorithm (EWOA). The major finding lies in an efficient hybridization of bio-inspired (WOA) and physics-based (EO) metaheuristic algorithms. Upon mathematical modelling, EWOA proposes a main architecture that combines WOA's encircling and net-bubble attacking mechanisms via EO's weight balance strategy. The proposed algorithm was tested on 23 classical, 28 constrained CEC 2017, 30 unconstrained CEC 2017, 10 CEC 2019, and 10 CEC 2020 benchmark problems, in comparison with six recently proposed state-of-the-art algorithms (including WOA and EO). EWOA outperforms other algorithms with the best statistical mean performance on 46 out of 101 functions and the most promising clustering data in the graph, respectively. The fact that EWOA could achieve best statistical SD performance on 2 of the total 5 benchmark sets proves that EWOA is competitively robust. EWOA can converge to the optimum before 50% iterations of most benchmark functions, achieving the fastest convergence rate compared to other algorithms. The major contribution thereby lies in the successful development of this hybrid algorithm, which yields better optimization efficiency than the original and other state-of-the-art algorithms in terms of statistics, convergence and clustering. [ABSTRACT FROM AUTHOR]

In this paper, we consider a closed market model. In this model the supply and the demand functions are restored by their price elasticities. We obtain sufficient conditions on nonuniqueness of equilibrium in this model. For several special cases of closed market models we get a criteria of equilibrium uniqueness. The obtained results are illustrated with the example of the market with two goods. [ABSTRACT FROM AUTHOR]

Assessment of fish stocks is especially important to avoid overfishing and obtain sustainable fishing policies, and there are many stock assessment methods such as XSA, VPA, BMS, CMSY, and MSVPA to analyze fish stocks. However, these assessment methods require an important amount of data for fish stocks such as diet data, natural mortality, fishing mortality, abundance index of species, predator ratio estimates, and so on. Unfortunately, we do not have such data for most of the fish stocks, and obtaining such data requires an important amount of money and time, but we still can predict important information about fish stocks such as biomass of fish stocks, the maximum sustainable yield, the biomass of fish lost or gained due to predator-prey relations, and even can track the effect of harvesting on predator-prey relations by building a mathematical model for fish populations and implementing a stability analysis. To obtain these outputs, we only need landing data and implement a parameter estimation constrained on stability conditions derived from the stability analysis of the mathematical model. Shortly, this study shows us how important stability analysis is to obtain important information about fish populations in the absence of important data. [ABSTRACT FROM AUTHOR]

The pressure relief door (PRD) is a vital structure to ensure the safety and reliability of the engine. This paper established a zero-dimensional transient simulation mathematical model to study the plenum compartment pressure threshold and maximum opening angle effects on the nacelle pressure relief process under different opening modes. Then, a computational fluid dynamics model verified by experimental literature data was used to simulate the nacelle pressure relief process and to determine the influence of two different opening modes on the force and discharge characteristics of the PRD. The results of this study show that different opening modes strongly impact the nacelle pressure relief process. Reducing the nacelle compartment pressure threshold of the PRD opening can reduce the time required for the pressure relief process to reach the equilibrium stage. Reducing the maximum opening angle may increase the nacelle compartment pressure during the equilibrium stage. In addition, under the same nacelle compartment pressure thresholds and maximum opening angles, the pressure relief process under the vertical opening mode can reach a lower nacelle compartment pressure during the pressure relief equilibrium stage compared to that under the horizontal opening mode. Therefore, the vertical opening mode is better than the horizontal opening mode. This paper provides two lower calculation costs and high accuracy research models for studying the nacelle pressure relief process. [ABSTRACT FROM AUTHOR]

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, R c , is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for R c . In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics. [ABSTRACT FROM AUTHOR]

A new mathematical model describing an equilibrium of a thermoelastic heterogeneous Kirchhoff–Love plate is considered. A corresponding nonlinear variational problem is formulated with respect to a two-dimensional domain with a cut. This cut corresponds to an interfacial crack located on a given part of the boundary of a flat rigid inclusion. The flat inclusion is described by a cylindrical surface. Due to the presence of the flat rigid inclusion in the plate, restrictions of the functions describing displacements to the corresponding curves satisfy special constraints having a linear form. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual non-penetration of opposite crack faces. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, an equivalent differential formulation is found. This article is part of the theme issue 'Non-smooth variational problems and applications'. [ABSTRACT FROM AUTHOR]

The flow in the far turbulent wake behind a body of revolution is studied with the use of a three-parameter turbulence model, which includes differential equations of the turbulent energy balance, transfer equation for the turbulent energy dissipation rate, and turbulent shear stress equation. Local equilibrium algebraic truncation of the transfer equation for the turbulent shear stress yields the known Kolmogorov–Prandtl relation. Under a certain restriction on the values of the empirical constants and for the law of time scale growth consistent with the mathematical model, this relation is a differential constraint of the model or an invariant manifold in the phase space of the corresponding dynamic system. The equivalence of the local equilibrium approximation and the condition of the zero value of Poisson's bracket for the normalized turbulent diffusion coefficient and defect of the averaged streamwise component of velocity is demonstrated. Results of numerical experiments are reported; they are found to be in good agreement with theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, role of chaotic systems with perpendicular line equilibrium, line equilibrium, and no-equilibrium is investigated by employing Mittage-Leffler kernel. The fractal-fractionalized mathematical and dynamical models have been observed for quasi-periodicity chaos and hyperchaos as well as simple periodicity chaos and hyperchaos. Each chaotic systems type is simulated on the basis on comparative analysis through Atangana-Baleanu fractal differential operator versus Atangana-Baleanu fractional differential operator. The numerical simulations have been performed by means of Adams-Bashforth-Moulton method for observing the controversial role of chaotic systems on the basis of phase portrait. The nonsingularity associate to the fractal fractional differentiation of Atangana-Baleanu has been introduced. Finally, 3D and 2D phase portraits of chaotic system with perpendicular line equilibrium, line equilibrium and no-equilibrium have been underlined to capture the similarities and differences among the depicted phase portraits parametrically. [ABSTRACT FROM AUTHOR]

• Propose a parking-size weibit (PSW) model for the parking choice with emerging shared parking services. • Propose a spatially correlated weibit (SCW) model for the destination choice with spatial information. • Address the spatial similarity and heterogeneity issues in the joint destination and parking choice. • Develop the combined SCW-PSW equilibrium model with an equivalent mathematical programming formulation. • Develop a partial linearization algorithm combined with an iterative balancing scheme for solving the SCW-PSW equilibrium model. This paper proposes a weibit-based equilibrium choice model for investigating the effect of the emerging shared parking services, which have recently received increasing interest, on combined destination location and parking choice behaviors. The model considers the features of shared parking services, including the avoidance of cruising to search for a parking space and limited supply of shared parking spaces. The spatial similarity issues of destination and parking choices, i.e., the correlations among spatially adjacent destination locations and the parking spaces around them, are separately considered through the advanced spatially correlated weibit (SCW) model and parking-size weibit (PSW) model, respectively. Subsequently, an equivalent mathematical programming (MP) formulation of the equilibrium SCW-PSW model is developed, which guarantees the existence and uniqueness of the solutions. Based on the MP formulation, a partial linearization algorithm embedded with the iterative balancing direction-finding scheme and self-regulated averaging line search scheme is developed to solve the proposed equilibrium model. Numerical examples are presented to illustrate the properties of the proposed model and its applicability to analyzing planning scenarios with different shared parking supplies. [ABSTRACT FROM AUTHOR]

There are five different forms of intervention presently realised by the Indonesian government in an effort to end the COVID-19 pandemic: vaccinations, social restrictions, tracings, testings, and treatments. In this paper, we construct a mathematical model of type SVEIQHR (susceptible-vaccinated-exposed-infected-quarantined-hospitalised-recovered) for the disease's spread in the country, which incorporates as parameters the rates of the above interventions, as well as the vaccine's efficacy. We determine the model's equilibria and basic reproduction number. Using the model, we formulate strategies by which the interventions should be realised in order to optimise their impact. The results show that, in a disease-free state, when the number of new cases rises, the best strategy is to implement social restrictions, whereas in an endemic state, if a near-lockdown policy is undesirable, carrying out vaccinations is the best strategy; however, efforts should be aimed not primarily towards increasing the vaccination rate, but towards the use of highefficacy vaccines. [ABSTRACT FROM AUTHOR]

In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick's second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data. [ABSTRACT FROM AUTHOR]

In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R0 and some concluding remarks. [ABSTRACT FROM AUTHOR]

Biosorption has great potential in removing toxic effluents from wastewater, especially heavy metal ions such as cobalt, lead, copper, mercury, cadmium, nickel and other ions. Mathematically modeling of biosorption process is essential for the economical and robust design of equipment employing the bioadsorption process. However, biosorption is a complex physicochemical process involving various transport and equilibrium processes, such as absorption, adsorption, ion exchange and surface and interfacial phenomena. The biosorption process becomes even more complex in cases of multicomponent systems and needs an extensive parametric analysis to develop a mathematical model in order to quantify metal ion recovery and the performance of the process. The biosorption process involves various process parameters, such as concentration, contact time, pH, charge, porosity, pore size, available sites, velocity and coefficients, related to activity, diffusion and dispersion. In this review paper, we describe the fundamental physical and chemical processes involved in the biosorption of heavy metals on various types of commonly employed biosorbents. The most common steady state and dynamic mathematical models to describe biosorption in batch and fixed-bed columns are summarized. Mathematical modeling of dynamic process models results in highly coupled partial differential equations. Approximate methods to study the sensitivity analysis of important parameters are suggested. [ABSTRACT FROM AUTHOR]

Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy. [ABSTRACT FROM AUTHOR]

In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in intra-host models neglects this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behaviour of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case. [ABSTRACT FROM AUTHOR]

The paper is devoted to examining the role of the shadow economy in the context of market equilibrium. The Walras theorem was used in order to highlight the role of the shadow economy in market equilibrium violation. Habitually, a majority of theories as well as models focus just on observed variables and latent factors are omitted. The shadow economy is an unprejudiced typical case in this respect. It exists in any economy and it very often influences market mechanisms significantly. A mathematical model was employed to exhibit dependence between the shadow economy and market equilibrium. Whenever the shadow economy is ignored in modeling market equilibrium, the market is proved to be balanced. The situation changes when the shadow economy is taken into account. Market equilibrium is difficult to be achieved. [ABSTRACT FROM AUTHOR]

We consider a mathematical model of a simply supported Euler–Bernoulli beam with an attached springmass system. The model is controlled by distributed piezo-actuators and a lumped force. We address the issue of asymptotic behavior of the solutions of this system driven by a linear feedback law. The precompactness of trajectories is established for the operator formulation of the closed-loop dynamics. Sufficient conditions for the strong asymptotic stability of the trivial equilibrium are obtained. [ABSTRACT FROM AUTHOR]

In this paper, an extended SIRB deterministic epidemiological model for Cholera was developed and strictly analysed to ascertain the impact of immigration in cholera transmission and to assess the suitability of the various control measures. The model was found to have two equilibria, namely, disease-free equilibrium (DFE) and a unique endemic equilibrium (EE). The local stability of the DFE and EE were found to be dependent on a certain epidemiological threshold known as the basic reproductive number, R 0 (number of secondary infections resulting from the introduction of a single infected individual into a population), in that DFE is stable when R 0 < 1 , whereas the EE is stable when R 0 > 1. Furthermore, we used the Lyapunov function and geometric approach respectively to show that the DFE and EE are globally asymptotically stable and that Cholera will persist in the population when R 0 > 1. Our model was fitted to Uganda Cholera cases (1999–2015). The best fit parameters were then used to carry out numerical simulation of the model. Specifically, the impact of the control over the long and short cycle transmission routes were found to be more effective than vaccination in combating the menace of Cholera in Uganda. Finally, the effects of immigration in the transmission of cholera were validated via numerical simulation using estimated and base line parameter values. [ABSTRACT FROM AUTHOR]

The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton–zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark–Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark–Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A numerical model based on large eddy simulation code supported with a laboratory experiment was used to explore the mechanism of scour and deposition process around a submerged L-head groyne at equilibrium stage of flow. The numerical model used the equilibrium bathymetry, which was obtained from an experiment conducted in the laboratory. The components of Horse Shoe vortex system (HV) including the presence of aperiodic oscillatory motions between back flow and zero flow modes near the groyne faces junction are explored. Formations of elliptical-shaped vortex tubes along detached shear layer (DSL) and their merging phenomenon at different time scales of flow are also investigated. Increase in vorticity magnitude towards bottom as compared to upper planes for instantaneous and mean flow field is identified. Near bed region, concentration of DSL profile towards submerged mound situated in the wake region emerges as dominating factor over HV system for the production of larger vorticity magnitude. Transportation of DSL eddies, their interaction with wake vortices and flow within reattachment zone are also focussed. To emphasize, this innovative study was conducted first time to fulfil the gap of exploring mechanism of scour and deposition process around such a complex geometry under submerged condition over scoured bed. [ABSTRACT FROM AUTHOR]

The high-static-low-dynamic stiffness vibration isolator has great advantages in vibration isolation because it can decrease the natural frequency of the system while keeping the load capability, but it is usually difficult to implement because of its complex structures and installation space constraints. A high-static-low-dynamic stiffness vibration isolator composed of a buckling circular plate and a traditional linear spring is proposed in this paper. The buckling circular plate works as the negative stiffness corrector paralleled with the linear spring, which can be integrated into the sleeve. If the load is chosen properly, the static equilibrium point will be at the initial quasi-zero stiffness point. However, any changes of the load will lead the equilibrium point deviating from the initial equilibrium point. The nonlinear mathematical model of high-static-low-dynamic stiffness vibration isolator considering load imperfection is developed and its force transmissibility is analyzed with the harmonic balance method and homotopy perturbation method. The influence rule of the system parameters on it is analyzed and the corresponding results show that the force transmissibility will exhibit complicated characteristics, depending on the load imperfection, damper, and excitation force. [ABSTRACT FROM AUTHOR]

Asymmetric property of the pinched hysteresis loop usually appears in a real memristor. To imitate this property, an asymmetric memristor emulator is constructed by an analog circuit consisting of a non-balance diode-bridge and a resistor-capacitor (RC) filter. By coupling this emulator to the classical Chua's circuit in parallel in both forward and reverse ways, two asymmetric memristive Chua's circuits are proposed and their mathematical models are established. Because of the symmetry between the forward and reverse circuits, the forward memristive Chua's (FAMC) circuit is focused on modelling the normalised system and investigating the equilibrium stability. With the FAMC system, several numerical plots are employed to discuss the parameter-dependent complex dynamics and initial-dependent coexisting behaviours. The numerical results manifest that there are three equilibrium points in the FAMC system, among which two non-zero equilibrium points are asymmetric, resulting in the emergence of asymmetric attractors. With the change of system parameters, the stability of one non-zero equilibrium point converts from unstable saddle-focus into stable node-focus, leading to the coexistence of multiple attractors. In addition, hardware experiments on a breadboard level are executed and the captured results well verify the numerical plots. [ABSTRACT FROM AUTHOR]

Pollutants and toxicants are released into the environment as a result of numerous industrial and other human activities. These dangerous discharges affect the resource biomass which eventually affects the biological species. In this paper, we have proposed and analyzed a non-linear mathematical model to study the effect of pollutant-affected resource biomass on biological species. Five dependent variables have been considered in the modelling process. The model has been analyzed analytically through equilibrium and stability analysis. It has been found that the environmental tax imposed on the polluters proves as an important measure to maintain the resource dependent biological species at a desirable level. Numerical simulation is also done to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic mathematical model for the transmission dynamics of Visceral leishmaniasis (VL) was formulated and analyzed. The basic reproductive number R0 was obtained using the next generation matrix method. The model which was parameterized using the 2011 cases of Visceral Leishmaniasis in South Sudan, was used to assess two control measures. Numerical simulation reveals that the exposed population is reduced by high detection rate, and low biting rate of sandflies. Further, our model simulation gave the values of the contact rate of susceptible human, α1 and the detection rate of new cases, σ at which the basic reproductive number is less than one, (R0 < 1), equal to one (R0 = 1) and greater than one (R0 > 1). [ABSTRACT FROM AUTHOR]

In this paper, we extend the classic SIR model to find an optimal lockdown policy to balance between the economy and people's health during the outbreak of COVID-19. In our model, we intend to solve a two phases optimisation problem: policymakers control the lockdown rate to maximise the overall welfare of the society; people in different health statuses take different decisions on their working hours and consumption to maximise their utility. We develop a novel method to estimate parameters for the model through various additional sources of data. We use the Cournot equilibrium to model people's behaviour. The analysis of simulation results provides scientific suggestions for policymakers to make critical decisions on when to start the lockdown and how strong it should be during the whole period of the outbreak. [ABSTRACT FROM AUTHOR]

Pneumonia is one of the leading causes of death worldwide, especially among children below 5 years, the elderly above 65 years and people with weaker immune system. It is usually referred to as the "captain of the men of death" because of the great toll it exacted on humanity. In this work, we examined the dynamics of the pneumonia disease from a mathematical perspective via a deterministic SEIR model. This consists of investigating the equilibrium, basic reproduction number, stability analysis, and bifurcation analysis. It is observed that the pneumonia free equilibrium is locally asymptotically stable if the basic reproduction number is less than one, and the pneumonia endemic equilibrium is globally asymptotically stable in the invariant region if the basic reproduction number is greater than one. The sensitivity analysis revealed that the rate of transmission and the rate at which exposed individuals become infectious are the most sensitive parameters, and the bifurcation analysis via the centre manifold theory revealed the presence of forward bifurcation. [ABSTRACT FROM AUTHOR]

In this present contribution, a simple chaotic oscillator based on a memcapacitor with only one equilibrium point is reported. The proposed oscillator consists of an inductor (only storage element) and a nonlinear active memcapacitor which is the key component responsible for the complex behaviors exhibited by the circuit. The resulting mathematical model is a simple jerk-type equation system that is easy to manipulate both analytically and numerically. The numerical results reveal the emergence of a plethora of phenomena such as period-doubling bifurcations, antimonotonicity, offset-boosting, and multistability giving rise to several kinds of coexisting attractors among which the coexistence of six stable states. The PSpice investigations confirm the real feasibility of the proposed circuit. The complexity of the phenomena and behaviors observed make the particularity of the proposed memcapacitor–inductor circuit and thus constitutes an enriching contribution in nonlinear dynamics. [ABSTRACT FROM AUTHOR]

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA). [ABSTRACT FROM AUTHOR]

This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that of the continuous BGK equation is proven. Numerical simulations are presented to validate the proposed mathematical model. [ABSTRACT FROM AUTHOR]