Order Delay Research Articles

Stability and bifurcation analysis of a fractional order delay differential equation involving cubic nonlinearity

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation Dαx(t)=δx(t−τ)−ϵx(t−τ)3−px(t)2+qx(t).We provide linearization of this system in a neighborhood of equilibrium points and propose linearized stability conditions. To discuss the stability of equilibrium points, we propose various conditions on the parameters δ, ϵ, p, q and τ. Even though there are five parameters involved in the system, we are able to provide the stable region sketch in the qδ−plane for any positive ϵ and p. This provides the complete analysis of stability of the system. Further, we investigate chaos in the proposed model. This system exhibits chaos for a wide range of delay parameter.

Optimal control of nonlinear fractional order delay systems governed by Fredholm integral equations based on a new fractional derivative operator

We aim to develop a direct transcription approach for solving a notable category of optimal control problems governed by nonlinear fractional Fredholm integral equations having delays in both input and output signals. The foundation of the new methodology is based on a multi domains decomposition scheme by utilizing the fractional-order Legendre functions. A new fractional derivative operator associated with the fractional basis is introduced by using the Caputo fractional derivative operator. With the use of derivative and delay operators, one can transform the dynamical system related to the fractional control problem into a new system containing algebraic equations. A wide variety of challenging test problems are studied to provide a detailed explanation of the designed approach.

New Oscillation Criteria of Nonlinear Second Order Delay Difference Equations

In the paper, we study some new criteria for the oscillation of the nonlinear second-order delay difference equations of the form varDelta (rleft( t right) ({varDelta xleft( t right) )}^{alpha })+qleft( t right) x^{beta }left( t-m+1 right) =0, via comparison with a second-order linear difference equation or a first-order linear delay difference equation whose oscillatory behavior is discussed intensively in the literature. The presented results essentially improve existing ones.

Development a Warehouse Management Information System

A warehouse management system (WMS) is a software application that helps control and manage the day-to-day operations in a warehouse. WMS software guides inventory receiving and put-away, optimizes picking and shipping of orders. This research has the objective to design a warehouse management information system in Hypertext Preprocessor language (PHP). The development methodology used is Rapid Application Development (RAD) with an object-oriented approach while the tool used in design is Unified Modeling Language (UML). Problems in the distributor of plumbing products are the increasingly large amount of stored information resulting in storing information in Excel files that no longer meet the requirements of retrieving and synthesizing information, as well as the storage of goods in the warehouse is disorganized leading to the increasing order processing time, which is one of the reasons of the increase in order delay rate. The solution of this problem focuses on implementing a management information system which helps to store and retrieve goods information (quantity, location,...), thereby reducing order processing time and increasing labor efficiency for businesses.

Dixon resultant theory for stability analysis of distributed delay systems and enhancement of delay robustness

This study scrutinizes the stability problem of linear time-invariant feedback control systems with a constant-coefficient, partial delay distribution from a new perspective, which is built on an equivalence between the system of interest and the one with two lumped delays. We aim to determine all the potential stability changing curves (PSCC) of the system in the domain of delays in order to make a non-conservative stability assessment. First, we propose the Dixon resultant-based frequency sweeping procedure to calculate the so-called kernel and offspring hypersurfaces (KOH) of the system. The superiority in the computational efficiency of this Dixon-type method is revealed by comparison with the Sylvester-type one. Second, we specifically tackle the standing root case for the singularity at the zero root, leading to what we call the standing root boundary (SRB). Then, we claim that the union of the KOH and SRB constitutes the PSCC of the system. With these, the stability map of the system is then created using the Cluster Treatment of Characteristic Roots paradigm. Furthermore, we declare the delay robustness is enhanced by the proposed control law. Finally, we demonstrate the effectiveness of the presented procedures over two example case studies by the Quasi-Polynomial mapping-based Root-finder routine as well as the Simulink-based simulation.

Arena Simulation of Spare Parts Inventory Management: A Case of A Telecom Managed Service Provider

Telecommunications and utilities companies, among other large service organisations, confront a slew of decision-making challenges, many of which are connected to the management of a variety of different resources. The management of spare parts and inventories is one of the most difficult resource management concerns that an organisation has to deal with on a regular basis. Their prompt availability may have a significant influence on the overall quality of the service and the level of client satisfaction. The purpose of the study was to assess the Spare Parts Inventory Management of XYZ company operating within the Ghanaian telecommunication ecosystem. Data on demand and inventory stock level was collected from the procurement department of XYZ company. The study adopted the use of the Arena Simulation model to analyze data collected from the XYZ company. The results of the analysis indicated that the procurement department is unable to meet the spare parts demand of the Passive department where the average order received from the department in a day is 6.08. Based on the findings of the study, it is recommended that the procurement department put in measure to receive and process orders in time. The reason for the delay in processing orders could be the less poor inventory management practices of the company. The study recommends that systems be adopted to track the inventory level of the company. Due to the stochastic nature of the demand from the passive department, the company should be proactive in the management of the demand by keeping the right stock level in order to meet the demand of the department in order to reduce the long down time. Key words: Spare parts, inventory, Arena Simulation, telecommunication DOI: 10.7176/EJBM/14-12-10 Publication date: June 30 th 2022

Nucleation delay in water-saturated rhyolite during decompression in shallow volcanic systems and its implications for ascent dynamics

We developed a model of feldspar nucleation delay during decompression in water-saturated rhyolite based on classical nucleation theory (CNT). With the thermodynamic and kinetic parameters proposed in this study, the model agrees with the experimental results of this study to within a factor of two. To account for the variety of conditions encountered by magma during ascent, we propose expanding the model, developed in this study for isothermal decompression, to a wider range of pressures and temperatures (i.e. non-isothermal conditions). We present new measurements of feldspar growth rates during decompression in water-saturated rhyolite, emphasizing the importance of accurately calculating the nucleation delay in order to estimate growth rates. Using these data, we propose a method for estimating the ascent rate of water-saturated rhyolite based on the nucleation delay of feldspar microlites. The findings of this study hold the promise of a better understanding of volcanic timescales during magma ascent in the conduit, as well as the possibility of extending our model to more complicated scenarios with changing pressure and temperature.

A Class of Seventh Order Hybrid Extended Block Adams Moulton Methods for Numerical Solutions of First Order Delay Differential Equations

This paper considers the computational solution of some first order delay differential equations (DDEs) using a class of seventh order Hybrid Extended Block Adams Moulton Methods (HEBAMM) without the application of interpolation techniques in evaluating the delay term. The delay term was evaluated by a valid expression of sequence. By matrix inversion techniques, the discrete schemes of the proposed method were obtained through its continuous derivations with the help of linear multistep collocation procedure. The convergence and stability analysis of the method were investigated. After the demonstration of the proposed method in solving some first order DDEs, it was observed that the higher step number k = 4 integrated with a hybrid extended future point performed better and faster in terms of efficiency, accuracy, consistency, convergence, region of absolute stability and Central Processing Unit Time (CPUT) than the lower step numbers k = 3 and 2 integrated with hybrid extended future points when compared with the exact solutions and other existing methods at fixed step size .

An approximation method and PID controller tuning for systems having integer order and non-integer order delay

In this study, an algebraic approximation method is proposed to investigate the stability analysis and time domain response of non-integer order delay systems. Besides, stabilizing Proportional Integral Derivative (PID) controllers are computed in the (kp,ki) plane for the fixed value of kd and a simple PID controller tuning method for the systems with integer order delay and non-integer order delay is presented. For this purpose, to obtain stable PID controller parameters in the (kp,ki) plane, the necessary equations are obtained using the stability region concept. A new design technique is proposed that facilitates the selection of the controller parameters from this region. This design technique is compared with the weighted geometrical center method (WGC). Both methods are used for the first time to the systems with non-integer order delay. Comparisons are also made with some other tuning methods in the literature. Considering the reasonable results obtained, the proposed method can be seen as a very advantageous design technique. Moreover, it provides an easy design procedure without any performance criteria restrictions such as gain margin, phase margin, maximum overshoot, etc. The only criterion here is to obtain the stability region. The simulation results include a detailed comparison of the WGC and the proposed method. Although the WGC seems to be superior in terms of performance, the computational load is considerably higher than the proposed method, which makes the proposed method quite sufficient for a simple and acceptable start.

Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies

A delay epidemic model is developed, with the susceptible population divided into three subclasses. In the main model, the well-known “Michaelis Menten Equation” is utilized to represent the effect of saturation. Infected, unaware, partially aware, and fully conscious compartments are included in the saturation incidence rates. The model includes a time delay to demonstrate the occurrence of Hopf Bifurcation. Following the formulation of a delay epidemic model, the local stability and the presence of Hopf bifurcation are investigated. The direction and stability of the Hopf bifurcation are then investigated. Furthermore, the Nyquist criterion is used to estimate the length of the time delay in order to maintain stability. An example is also presented to highlight the current research work's findings. Finally, appropriate control techniques are introduced to aid policymakers in disease control. The “Pontryagin's maximum principle” is the major tool utilized in the optimal control part.

Robust stabilization and synchronization in a network of chaotic systems with time-varying delays

In this paper, a novel controller technique is derived for the network synchronization of chaotic systems with time-varying delay. The stabilization of the complex chaotic systems is achieved by considering an appropriate Krasovskii-Lyapunov functional in order to find the asynchronous robust stabilization law and fast switching topology. In a similar way, the asynchronous technique is based on an appropriate switching topology in order to synchronize the chaotic systems. The time-varying delays occur in different systems which increase the complexity of the synchronization. So for this reason, an asynchronous controller is designed by considering the time-varying delays in order to avoid instability or deteriorate performance of the whole chaotic systems. The remarkable finding of this study is that the robust controller considers the uncertainties on each complex chaotic systems node until an exact synchronization is achieved while switching the action of the controller synchronization and the chaotic node dynamics of the studied complex systems. Finally, numerical examples are considered on chaotic Rössler systems to test and validate the obtained theoretical results.

Sectoral impact of COVID-19 on micro enterprises with special reference to Kerala

The aftershocks of the novel corona virus had shut down several sectors in the global economy. Due to challenges like raw material shortage, lack of demand, high turnover, delay in bill payments and orders caused by the lockdown restrictions, the micro enterprises were seriously affected the most. On the basis of the background, the present study deals with sectoral impact of Covid crisis on the micro enterprises. Challenges with respect to production, employment, finance and sales are discussed in the paper. Business like Kudumbashrees, handicraft, handloom and dairy farm, covering the whole Kerala with 14 districts, are considered to be more vulnerable to the negative shocks and are hence taken onto the study to identify the kind of factors that led to the hampering of the business. One of the major objectives of this study is to identify and analyse the challenges faced by the micro enterprises during Covid-19. The study also needs to understand the coping mechanisms adopted by these micro-enterprises during the crises. Primary data collection, via questionnaires and telephonic interview, is taken for the study where in 80 is chosen as the sample size.

Identifying and Understanding the Non-Clinical Impacts of Delayed or Cancelled Surgery in Order to Inform Prioritisation Processes: A Scoping Review.

The COVID-19 pandemic has resulted in significant delays to non-urgent elective surgery. Decision making regarding prioritisation for surgery is currently informed primarily by clinical urgency. The ways in which decision making should also consider potential social and economic harm arising from surgical delay are currently unclear. This scoping review aimed to identify evidence related to (i) the nature and prevalence of social and economic harm experienced by patients associated with delayed surgery, and (ii) any patient assessment tools that could measure the extent of, or predict, such social and economic harm. A rapid scoping review was undertaken following JBI methodological guidance. The following databases were searched in October 2020: AMED; BNI; CINAHL; EMBASE; EMCARE; HMIC; Medline; PsychINFO, Cochrane, and the JBI. A total of 21 publications were included. The findings were categorised into five themes: (i) employment, (ii) social function and leisure, (iii) finances, (iv) patients’ experiences of waiting, and (v) assessment tools that could inform decision making. The findings suggest that, for some patients, waiting for surgery can include significant social, economic, and emotional hardship. Few validated assessment tools exist. There is an urgent need for more research on patients’ experiences of surgical delay in order to inform a more holistic process of prioritising people on surgical waiting lists in the COVID-19 pandemic recovery stages.

Dilaton-axion black hole lensing and its relativistic images

Appraising a massive dark object at the centre of our galaxy, we analyse gravitational lensing effect for dilaton-axion black hole. We have explored angular positions, magnifications, time delay, effective deflection angle as well as differential time delay of both primary and secondary first order as well as second order images for such kind of black hole spacetime.

Exponential stability for a system of second and first order delay differential equations

Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a1(t)ẋ(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0is studied, where indirect feedback control u̇(t)+b1(t)u(g1(t))+b2(t)x(g2(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.

Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations

In this paper we deal with numerical solutions for a class of nonlinear second order delay differential equations. In order to approximate this problems, the block methods consisting of generalized Störmer-Cowell methods are proposed. The error analysis indicates, under appropriate conditions, the numerical schemes can have convergence of order p when they are consistent of order p. Finally, some numerical experiments are performed to illustrate accuracy of proposed methods and corresponding theoretical results.

Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations

Among many other factors that affect the preventive interventions to any infectious disease, not reporting timely in a hospital is also one of the catastrophic behavior of human beings in any society. Similarly, masses who do not report make it difficult for healthcare researchers to measure the actual data and develop prevention strategies, accordingly. Therefore, there is a critical need to structure a potential epidemic model with the unreported class of individuals. This novel idea is deliberated in this paper to study the profiles of the epidemic model of virulent diseases due to the individuals that report timely and those who don't report in hospitals for any reason. Mathematically, a system of seven equations is taken into consideration, which describes the susceptible individuals, exposed, people who do not report to the hospital and those who report to the hospital, and individuals who are quarantined, infected, and recovered. So, with the consideration of new compartments, the conventional SIR epidemic model expands to SEURRPQIR. The innovative design is made more realistic by utilizing proportional fractional-order differential equations with time delay. A special simplified expansion of this derivative reduces its computational cost and produces the results with fractional index, which helps to predict each fractional change. In addition, an optimal control methodology is also carried out to analyze the effectiveness of the awareness campaign in shifting the unreported individuals to the reported class, with optimal cost function for the unreported cases. Discussions are supported through the very recent deadly pandemic as an example to conclude the practical advantage of the model. The sensitivity analysis of basic reproduction numbers based on effective awareness campaigns is also the part of this study, which infers public awareness campaigns may be devised to motivate and guide such individuals to approach any healthcare center or a hospital.

Machine Selection Application in a Hard Chrome Plating Industry Using Fuzzy SWARA and Fuzzy ARAS Methods

Machines are one of the most important production elements used by companies in the production phase. Sudden deterioration in machinery creates a process that can lead to a production halt and therefore a delay in orders. For this reason, enterprises decide to replace their old machines with newer technological machines. This replacement decision is not easy as it includes many criteria and there are many alternative machines on the market. From this point of view, in this study, a real-life application of a company's machinery purchase was made with fuzzy SWARA and fuzzy ARAS methods based on multi-criteria decision-making method. Criterion weights were determined by the fuzzy SWARA method. In the evaluation of alternative machines, the fuzzy ARAS method was taken into consideration. In the study, the criteria determined by the company manager and his team in line with the company needs were taken into consideration. Afterward, four machines were determined among the most suitable machines in the market and frequently used. Finally, calculations were made to find the machine that best meets the criteria required by the company among these machines. As a result of the calculations, the machine needed by the company was decided and the results were interpreted. Key Words: Machine Selection, Multi-Criteria Decision Making, Fuzzy SWARA, Fuzzy ARAS JEL Classification: M10, D70, D81

Conditions for the Boundness of the Solution for Second Order Linear Delay Differential Equations

It is well known that a solution to a second order differential equation with roots of its characteristic equation in the right half plane is unbounded. If a delay of the right magnitude is introduced into the equation the solution is bounded. This paper investigates this phenomenon by imbedding a second order differential equation with first order delay by embedding the equation in a field of equivalent classes of quotients of polynomials in the modified differential and delay operator over the real field.

The Computational Solution of First Order Delay Differential Equations Using Second Derivative Block Backward Differentiation Formulae

In this paper, we implemented second derivative block backward differentiation formulae methods in solving first order delay differential equations without the application of interpolation methods in investigating the delay argument. The delay argument was evaluated using a suitable idea of sequence which we incorporated into some first order delay differential equations before its numerical evaluations. The construction of the continuous expressions of these of block methods was executed through the use of second derivative backward differentiation formulae method on the bases of linear multistep collocation approach using matrix inversion method to derive the discrete schemes. After the numerical experiments, the new proposed method was observed to be convergent, stable and less time consuming. From the numerical solutions obtained, the scheme for step number k = 4 performed better in terms of accuracy than that of the schemes for step numbers k = 3 and 2 when compared with other existing methods.