scholarly journals Stability analysis of a simple mathematical model for school bullying

2022 ◽  
Vol 7 (4) ◽  
pp. 4936-4945
Author(s):  
H. A. Ashi ◽  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
School Bullying ◽  
Drop Out ◽  
Simple Mathematical Model ◽  
Globally Asymptotically Stable ◽  
School Drop Out ◽  
New Criterion ◽  
The Mathematical Model ◽  
Commit Suicide

<abstract><p>School bullying is a highly concerned problem due to its effect on students' academic achievement. The effect might go beyond that to develop health problems, school drop out and, in some extreme cases, commit suicide for victims. On the other hand, adolescents who continuously bully over time are at risk of becoming involved in gang membership and other types of crime. Therefore, we propose a simple mathematical model for school bullying by considering two variables: the number of victims students and the number of bullies students. The main assumption employed to develop the mathematical model is that school policy bans bullying and expels students who practice this behavior to maintain a constructive educational environment within the school. We show that the model has two equilibrium points, and that both equilibrium points are locally and globally asymptotically stable under certain conditions. Also, we define a threshold parameter with a new criterion called the bullying index. Furthermore, we show that the model exhibits the phenomena of transcritical bifurcation subject to the bullying index. All the findings are supported with numerical simulations.</p></abstract>

scholarly journals Experimental and Mathematical Model for the Antimalarial Activity of Methanolic Root Extract of Azadirachta indica (Dongoyaro) in Mice Infected with Plasmodium berghei NK65

2020 ◽  
pp. 68-82
Author(s):  
Adeniyi Michael Olaniyi ◽  
Momoh Johnson Oshiobugie ◽  
Aderele Oluwaseun Raphael
Keyword(s):  
Mathematical Model ◽  
Azadirachta Indica ◽  
Plasmodium Berghei ◽  
Antimalarial Activity ◽  
Equilibrium Points ◽  
Standard Procedure ◽  
Root Extract ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Group B

The study determines the experimental and mathematical model for the anti-plasmodial activity of methanolic root extract of Azadirachta indica in Swiss mice infected with Plasmodium berghei NK65. Phytochemical analyses, antimalarial activity of the methanolic root extract of A. indica was determined in mice infected with Plasmodium berghei NK65 using standard procedure. Liver biomarker enzymes were also determined. The model P. berghei induced free and P. berghei infected equilibrium were determined. The stability of the model equilibrium points was rigorously analyzed. The phytochemicals present in the extract include: alkaloid, flavonoid, saponin and phenolic compounds etc. The experimental study consists of five groups of five mice each per group. Group A, B, C, D and E were healthy, infected without treatment, infected mice treated with fansidar (10 mg/kg), chloroquine (10 mg/kg) and 250 mg/kg body weight of A. indica methanolic root extract respectively. The extract showed anti-plasmodial activity of 73.96%. The result was significant when compared with group B mice, though it was lower than that exhibited by fansidar (88.91%) and chloroquine (92.18%) for suppressive test. There were significant decrease (P<0.05) in plasma AST and ALT levels in the treated infected mice compared to the infected untreated mice. The results of the model showed that the P.berghei induced free equilibrium is locally and globally asymptotically stable at threshold parameter,  less than unity and unstable when  is greater than unity. Numerical simulations were carried out to validate the analytic results which are in agreement with the experimental analysis of this work.

scholarly journals Hybrid Secondary Suspension Systems

2009 ◽  
Vol 16 (5) ◽  
pp. 467-480 ◽  
Author(s):  
Nader Vahdati ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Vibration Absorbers ◽  
Simple Mathematical Model ◽  
System Behavior ◽  
Engine Mounts ◽  
Suspension Systems ◽  
Tuned Vibration Absorbers ◽  
Simulation Results ◽  
Secondary Suspension ◽  
The Mathematical Model

Passive fluid mounts are used in the fixed wing applications as engine mounts. The passive fluid mount is placed in between the engine and the fuselage to reduce the cabin's structure- borne noise and vibration generated by the engine.To investigate the benefits of passive fluid mounts used in conjunction with tuned vibration absorbers (TVA), a simple mathematical model is developed. This mathematical model includes the mathematical model of a passive fluid mount, a TVA, and a spring representing the fuselage structure. The simulation results indicate that when passive fluid mounts are used in conjunction with TVAs, an active suspension system behavior is nearly created.

scholarly journals Mathematical Modeling of the Fracture Toughness of Phenol Formaldehyde Composites Reinforced with E-Spheres

2009 ◽  
Vol 79-82 ◽  
pp. 1165-1168
Author(s):  
H. Ku ◽  
W. Xiang ◽  
N. Pattarachaiyakoop
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The fracture toughness of SLG filled phenolic composites have been determined by short bar tests. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the fracture toughness model using the data obtained from experiments. From experiments, it was found that the trend of the fracture toughness of the samples cured conventionally was similar to that cured in microwaves; it is therefore possible to predict the fracture toughness of the samples cured in microwaves from shifting the mathematical model generated for fracture toughness of samples post-cured in conventional oven. The shifted model represented the fracture toughness of the samples cured in microwaves vey well.

scholarly journals A simple mathematical model for Batesian mimicry

2005 ◽  
Vol 2005 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Terence R. Blows ◽  
Barry J. Wimmer
Keyword(s):  
Mathematical Model ◽  
Full Range ◽  
Logistic Map ◽  
Period Doubling ◽  
Species Interaction ◽  
Batesian Mimicry ◽  
Simple Mathematical Model ◽  
Predator Prey ◽  
The Mathematical Model ◽  
Period Doubling Bifurcations

A simple mathematical model is presented for Batesian mimicry, which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.

scholarly journals Optimisation of a clam bunk skidder from the emission production point of view

2012 ◽  
Vol 58 (No. 4) ◽  
pp. 136-141
Author(s):  
A. Janeček ◽  
R. Adamovský
Keyword(s):  
Mathematical Model ◽  
Production System ◽  
Operating Performance ◽  
Point Of View ◽  
Optimal Rate ◽  
Simple Mathematical Model ◽  
Operation Performance ◽  
The Mathematical Model

This article presents a proposal of a simple mathematical model for minimisation of the production of extraneous substances as a function of the rate of operation performance of a production system. The model is then verified by operation tests of the Terri 2040 clam bunk skidder and by determining the system&rsquo;s optimal rate of performance from the point of view of production of SO<sub>2</sub>, HC and NO<sub>x </sub>emissions. The operation tests conducted to verify the mathematical model have confirmed that conditions can be determined for the production system at which it produces minimum emissions. Min. values of SO<sub>2</sub>, and HC were achieved at approximately the same rate of performance of the clam bunk skidder. Minimum values of NO<sub>x </sub>were achieved at significantly higher rate of performance of the equipment. At the calculated optimal rate of operating performance of the Terri 2040 clam bunk skidder, the values of the produced emissions were determined per m<sup>3</sup> of timber: SO<sub>2</sub> = 1.00035 g/m<sup>3</sup>, HC = 7.796 g/m<sup>3</sup> and NO<sub>x</sub> = 0.277 g/m<sup>3</sup>.

scholarly journals A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

2020 ◽  
Vol 497 (1) ◽  
pp. 405-415
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Power Density Spectrum ◽  
Periodic Oscillations ◽  
Density Spectrum ◽  
X Ray ◽  
Almost All ◽  
The Mathematical Model

ABSTRACT The X-ray emission from the microquasar GRS 1915+105 shows, together with a very complex variability on different time-scales, the presence of low-frequency quasi-periodic oscillations (LFQPOs) at frequencies lower than ∼30 Hz. In this paper, we demonstrate that these oscillations can be consistently and naturally obtained as solutions of a system of two ordinary differential equations, which is able to reproduce almost all variability classes of GRS 1915+105. We modified the Hindmarsh–Rose model and obtained a system with two dynamical variables x(t), y(t), where the first one represents the X-ray flux from the source, and an input function J(t), whose mean level J0 and its time evolution is responsible of the variability class. We found that for values of J0 around the boundary between the unstable and the stable interval, where the equilibrium points are of spiral type, one obtains an oscillating behaviour in the model light curve similar to the observed ones with a broad Lorentzian feature in the power density spectrum and, occasionally, with one or two harmonics. Rapid fluctuations of J(t), as those originating from turbulence, stabilize the LFQPOs, resulting in a slowly amplitude modulated pattern. To validate the model, we compared the results with real RXTE data, which resulted remarkably similar to those obtained from the mathematical model. Our results allow us to favour an intrinsic hypothesis on the origin of LFQPOs in accretion discs ultimately related to the same mechanism responsible for the spiking limit cycle.

scholarly journals A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

2001 ◽  
Vol 35 (3) ◽  
pp. 224-231 ◽  
Author(s):  
Hyun M Yang
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Global Warming ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Compartment Model ◽  
Malaria Risk ◽  
Model Parameters ◽  
Socioeconomic Conditions ◽  
The Mathematical Model

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

scholarly journals Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points

2021 ◽  
Vol 11 (2) ◽  
pp. 788
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Talal Bonny ◽  
Sen Zhang ◽  
Sukono ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Field Programmable Gate Array ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Intrinsic Properties ◽  
Chaotic Dynamical System ◽  
Chaotic Model ◽  
Field Programmable ◽  
The Mathematical Model ◽  
New System

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).

scholarly journals Fundamentals of Synthesized Optimal Control

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 21
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko ◽  
Vladimir Serebrenny ◽  
Peter Zentay
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Method ◽  
Direct Method ◽  
Equilibrium Points ◽  
Control Object ◽  
Optimal Control Method ◽  
Optimal Value ◽  
New Formulation ◽  
The Mathematical Model

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

The Mathematical Model of Online Quenching for Extruding Bar of 6061 Aluminum Alloy

2011 ◽  
Vol 117-119 ◽  
pp. 1798-1801
Author(s):  
Yi Lin ◽  
De Zhi Li ◽  
Jian Min Zeng ◽  
Ping Chen ◽  
Li Hua Liang
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Aluminum Alloy ◽  
Simple Mathematical Model ◽  
Extrusion Speed ◽  
6061 Aluminum Alloy ◽  
Different Temperatures ◽  
Set Up ◽  
The Mathematical Model ◽  
Quenching Apparatus

A simple mathematical model that correlates the temperature and extrusion speed of a 6061 aluminum bar extruded from the die has been established based on the principle of heat transfer in this paper. The 6061 alloy bar is extruded from the die orifice and is cooled through heat exchanged between the bar and ambient. The temperature of the bar decreases as the distance increases away from the die orifice. The more rapidly the temperature drops, the slower the extrusion speed is. A flexible online quenching apparatus has been set up before the critical quenching position to guarantee good supersaturation of alloying elements. The calculations have shown that at the extrusion speeds of 10m/min, 15 m/min and 20 m/min, the critical quenching positions are 0.44m, 0.88m and 1.30m from the die orifice, respectively for the temperature of 520°C; and for the different temperatures, the critical quenching positions from the die orifice are 0.66m, 1.31m, 1.95m at 530°C and 0.88m, 1.75m, 2.6m at 540°C, respectively.

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