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On the Stability of Four Dimensional Lotka-Volterra Prey-Predator System
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The aim of this work is to study a modified version of the four-dimensional Lotka-Volterra model. In this model, all of the four species grow logistically. This model has at most sixteen possible equilibrium points. Five of them always exist without any restriction on the parameters of the model, while the existence of the other points is subject to the fulfillment of some necessary and sufficient conditions. Eight of the points of equilibrium are unstable and the rest are locally asymptotically stable under certain conditions, In addition, a basin of attraction found for each point that can be asymptotically locally stable. Conditions are provided to ensure that all solutions are bounded. Finally, numerical simulations are given to verify and support the obtained theoretical results.

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Publication Date
Wed Dec 25 2024
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of different palatal vault shapes and woven glass fiber reinforcement on dimensional stability of high impact acrylic denture base [part II]
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Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture. The aim of study is to evaluate the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on linear dimensional change and effect of palatal vault shapes on linear dimensional changes of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymerized high impact acrylic resin maxillary denture base were fabri

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Publication Date
Wed Dec 25 2024
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of different palatal vault shapes and woven glass fiber reinforcement on dimensional stability of high impact acrylic denture base [Part I]
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Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture.This study evaluated tostudy the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on adaptation or gap space between the denture base and the stone cast and compare with non-fiber reinforcement and effect of palatal vault shapes on adaptation of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymeri

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Dynamical Behavior of Two Predators-One Prey Ecological System with Refuge and Beddington –De Angelis Functional Response
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     The dynamical behavior of an ecological system of  two predators-one prey updated with incorporating prey refuge and Beddington –De Angelis functional response had been studied in this work, The essential mathematical features of the present model have been studied  thoroughly. The system has local and global stability when certain conditions are met.  had been  proved respectively.  Further, the system has no saddle node bifurcation but transcritical bifurcation and Pitchfork bifurcation are satisfied while the Hopf bifurcation does not occur. Numerical illustrations are performed  to validate the model's applicability under consideration. Finally, the results are included in the form of points in agreement with the obt

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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Volterra Runge- Kutta Methods for Solving Nonlinear Volterra Integral Equations
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In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

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Publication Date
Fri Jan 01 2016
Journal Name
International Journal Of Mathematics Trends And Technology (ijmtt)
Some Statistical Properties of the Solutions of a System of two dimensional Integral Equations contains Beta distribution
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Publication Date
Sun Mar 02 2008
Journal Name
Baghdad Science Journal
The influence of prey density on the numerical response of Chrysoperla mutata MacLachlan
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The numerical response of Chrysoperla mutata MacLachlan was achieved by exposing the larvae of the predators to various densities of dubas nymphs Ommatissus lybicus DeBerg. Survival rate of predators’ larvae and adults emergence increased with increasing consumption . Repriductive response of predator was highly correlated with the amount of food consumed (+0.996).

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Publication Date
Fri Jan 01 2016
Journal Name
International Journal Of Advanced Research
ON STABILITY AND THE BOUNDEDNESS OF THE ZERO SOLUTION OF FIFTH ORDER
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This paper is illustrates the sufficient conditions of the uniformly asymptotically stable and the bounded of the zero solution of fifth order nonlinear differential equation with a variable delay τ(t)

Publication Date
Sun Jan 01 2023
Journal Name
Communications In Mathematical Biology And Neuroscience
The dynamics of a delayed ecological model with predator refuge and cannibalism
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This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

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Publication Date
Mon Aug 01 2022
Journal Name
Journal Of Physics: Conference Series
The local bifurcation analysis of two preys stage-structured predator model with anti-predator behavior
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Abstract<p>This paper deals with two preys and stage-structured predator model with anti-predator behavior. Sufficient conditions that ensure the appearance of local and Hopf bifurcation of the system have been achieved, and it’s observed that near the free predator, the free second prey and the free first prey equilibrium points there are transcritical or pitchfork and no saddle node. While near the coexistence equilibrium point there is transcritical, pitchfork and saddle node bifurcation. For the Hopf bifurcation near the coexistence equilibrium point have been studied. Further, numerical analysis has been used to validate the main results.</p>
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Publication Date
Mon Jan 01 2024
Journal Name
Communications In Mathematical Biology And Neuroscience
Effects of fear and refuge strategy dependent on predator in food web dynamics
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