]>
2019
12
12
ISSN 2008-1898
90
Stability analysis of a tritrophic model with stage structure in the prey population
Stability analysis of a tritrophic model with stage structure in the prey population
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en
We analyze the role of the age structure of a prey
in the dynamics of a tritrophic model. We study the effect of predation
on a non-reproductive prey class, when the reproductive class of the prey has
a defense mechanism. We consider two cases accordingly to the interaction between predator and reproductive class of the prey. In the first case, the functional response is Holling type II and it is possible to show up to two positive equilibria. When we consider a defense mechanism the functional response is Holling type IV. In both cases, we show sufficient parameter conditions to have a stable limit cycle obtained by a supercritical Hopf bifurcation. Some numerical simulations are carried out.
765
790
Gamaliel
Blé
División Académica de Ciencias Básicas
México
gble@ujat.mx
Miguel Angel
Dela-Rosa
División Académica de Ciencias Básicas
México
madelarosaca@conacyt.mx
Iván
Loreto-Hernández
División Académica de Ciencias Básicas
México
iloretohe@conacyt.mx
Hopf's Bifurcation
tritrophic model
coexistence of species
prey age structure
Article.1.pdf
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]
Langevin equation involving one fractional order with three-point boundary conditions
Langevin equation involving one fractional order with three-point boundary conditions
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en
In this paper, we investigate a class of nonlinear Langevin equation involving one fractional order \(\alpha\in(0, 1]\) with three-point boundary conditions. By the Banach contraction principle and Krasnoselskii's fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.
791
798
Ahmed
Salem
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
ahmedsalem74@hotmail.com
Faris
Alzahrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Lamya
Almaghamsi
Department of Mathematics, Faculty of Science
Department of Mathematics
King Abdulaziz University
University of Jeddah
Saudi Arabia
Saudi Arabia
Fractional Langevin equations
fixed point theorem
existence and uniqueness
Article.2.pdf
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A. Salem, F. Alzahrani, L. Almaghamsi, Fractional Langevin equation with nonlocal integral boundary condition, Mathematics, 7 (2019), 1-10
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Z. F. Zhou, Y. Qiao, Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions, Bound. Value Probl., 2018 (2018), 1-10
]
Generalized inverse Lindley power series distributions: modeling and simulation
Generalized inverse Lindley power series distributions: modeling and simulation
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en
In this paper, we introduce a new generalization of a class of inverse Lindley distributions called the generalized inverse Lindley power series (GILPS) distribution. This class of distributions is obtained by compounding the generalized class of inverse Lindley distributions with the power series family of distributions. The GILPS contains several lifetime subclasses such as inverse Lindley power series, two parameters inverse Lindley power series, and inverse power Lindley power series distributions. It can generate many statistical distributions such as the inverse power Lindley Poisson distribution, the inverse power Lindley geometric distribution, the inverse power Lindley logarithmic distribution, and the inverse power Lindley binomial distribution. The proposed class has flexibility in the sense that it can generate new lifetime distributions as well as some existing distributions. For the proposed class, several properties are derived such as hazard rate function, limiting behavior, quantile function, moments, moments generating function, and distributions of order statistics. The method of maximum likelihood estimation can be used to estimate the model parameters of this new class. A simulation for a selective model will be discussed. At the end, we will demonstrate applications of three real data sets to show the flexibility and potential of the new class of distributions.
799
815
Said H.
Alkarni
Department of Quantitative Analysis
King Saud University
Saudi Arabia
salkarni@ksu.edu.sa
Generalized inverse Lindley power series distributions
inverse Lindley power series distributions
inverse power Lindley power series distribution
Article.3.pdf
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S. H. Alkarni, Extended inverse Lindley distribution: properties and application, Springer-Plus, 4 (2015), 1-13
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]
Controllability and observability of fuzzy matrix discrete dynamical systems
Controllability and observability of fuzzy matrix discrete dynamical systems
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en
In this paper, sufficient conditions for the controllability of the fuzzy dynamical discrete system with the use of fuzzy rule base are established. Further, a sufficient condition for the fuzzy dynamical discrete system to be observable is constructed. The main advantage of this approach is that the rule base for the initial value can be determined without actually solving the system. Difference inclusions approach is adopted in the construction of these conditions. All the established theories are consolidated and explained with the help of examples.
816
828
Charyulu L. N.
Rompicharla
Department of Mathematics
V. R. Siddhartha Engineering College
India
narayanarompicharla@gmail.com
Venkata Sundaranand
Putcha
Department of Mathematics
Rayalaseema University
India
anand_putcha@yahoo.com
G. V. S. R.
Deekshithulu
Department of Mathematics
JNTU College of Engineering
India
deekshitulu_g@yahoo.com
Fuzzy difference equations
fuzzy rule
controllability
observability
discrete dynamical systems
Article.4.pdf
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A. Alwadie, H. Ying, H. Shah, A Practical two-input two-output Takagi-Sugeno fuzzy controllers, Int. J. Fuzzy Syst., 5 (2003), 123-130
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]
Some recurrence relations of poly-Cauchy numbers
Some recurrence relations of poly-Cauchy numbers
en
en
Poly-Cauchy numbers \(c_n^{(k)}\) (\(n\ge 0\), \(k\ge 1\)) have explicit expressions in terms of the Stirling numbers of the first kind. When the index is negative, there exists a different expression. However, the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\) seem quite irregular for a fixed integer \(k\ge 2\).
In this paper we establish a certain kind of recurrence relations among the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\), analyzing the structure of poly-Cauchy numbers. We also study those of poly-Cauchy numbers of the second kind, poly-Euler numbers, and poly-Euler numbers of the second kind. Some different proofs are given.
As applications, some leaping relations are shown.
829
845
Takao
Komatsu
Department of Mathematical Sciences, School of Science
Zhejiang Sci-Tech University
China
komatsu@zstu.edu.cn
Poly-Cauchy numbers
poly-Euler numbers
recurrence
leaping relations
Vandermonde's determinant
Article.5.pdf
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T. Arakawa, T. Ibukiyama, M. Kaneko, Bernoulli numbers and zeta functions. With an appendix by Don Zagier, Springer, Tokyo (2014)
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]
Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud
Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud
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en
In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gas-dust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.
846
855
Mohammed
Abobaker
Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics
St. Petersburg Polytechnic University
Russia
mhmdbb@yahoo.com
Hydrodynamics
non-linear PDE
Cole-Hopf method
gravitating system gas-dust cloud
Article.6.pdf
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