2017
5
2
0
0
Effects of ionic parameters on behavior of a skeletal muscle fiber model
2
2
All living cells have a membrane which separates inside the cell from it's outside. There is a potential difference between inside and outside of the cell. This potential difference will change during an action potential. It is quite common to peruse action potentials of skeletal muscle fibers with the HodgkinHuxley model. Since Hodgkin and Huxley summarized some controlling currents like inward rectifier current or chloride current as a leak current when we try to study the sensitivity of model to some parameters we lose some details. In this paper we use a model which contains sodium, potassium, chloride, NaK pump, and inward rectifier currents. Firstly, we find critical point of the system, and discuss on how action potential changes for different initial values of variables. Then we study sensitivity of the critical point and maximum of potential to different parameters.
1

77
88


Samaneh
Shahi
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University
Iran
samanesh7@gmail.com


Hossein
Kheiri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University
Iran
hkheiri@tabrizu.ac.ir
action potential
sensitive analysis
skeletal muscle
Numerical solution of nonplanar Burgers equation by Haar wavelet method
2
2
In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the nonplanar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the nonplanar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a finite number of variables. The solution obtained by Haar wavelet collocation method is compared with that obtained by finite difference method and are found to be in good agreement. Shock waves are found to be formed due to nonlinearity and dissipation. We have analyzed the effects of nonplanar and nonlinear geometry on shock existence. We observe that nonplanar shock structures are different from planar ones. It is of interest to find that Haar wavelets enable to predict the shock structure accurately.
1

89
118


Sumana
Shesha
Bangalore University
Bangalore University
Iran
sumana.shesha@gmail.com


Achala L.
Nargund
Department of Studies in Mathematics, Karnatak University, Dharwad, India
Department of Studies in Mathematics, Karnatak
Iran
anargund1960@gmail.com


Nagendrappa M.
Bujurke
Department of Studies in Mathematics, Karnatak University, Dharwad, India
Department of Studies in Mathematics, Karnatak
Iran
bujurke@yahoo.com
Haar wavelets
nonplanar Burgers equation
quasilinearization
collocation points
finite difference
cylindrical and spherical geometry
Hopf bifurcation analysis of a diffusive predatorprey model with MonodHaldane response
2
2
In this paper, we have studied the diffusive predatorprey model with MonodHaldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system which are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are also presented.
1

119
136


Sambath
Muniyagounder
Department of Mathematics, Periyar University, Salem636011, India
Department of Mathematics, Periyar University,
Iran
sambathbu2010@gmail.com


Ramajayam
Sahadevan
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai600005, India
Ramanujan Institute for Advanced Study in
Iran
ramajayamsaha@yahoo.co.in
Stability
preypredator
MonodHaldane response
Hopf bifurcation
A mathematical model for treatment of bovine brucellosis in cattle population
2
2
Brucellosis is an infectious bacterial zoonosis of public health and economic significance. In this paper, a mathematical model describing the propagation of bovine brucellosis within cattle population is formulated. Model analysis is carried out to obtain and establish the stability of the equilibrium points. A threshold parameter referred to as the basic reproduction number $mathcal{R}_{0}$ is calculated and the conditions under which bovine brucellosis can be cleared in the cattle population are established. It is found out that when $mathcal{R}_{0}<1,$ the disease can be eliminated in the cattle population or persists when $mathcal{R}_{0}>1$. Using Lyapunov function and Poincair'{e}Bendixson theory, we prove that the diseasefree and endemic equilibrium, respectively are globally asymptotic stable. Numerical simulation reveals that control measures should aim at reducing the magnitude of the parameters for contact rate of infectious cattle with the susceptible and recovered cattle, and increasing treatment rate of infected cattle.
1

137
152


Julius
Tumwiine
Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda
Department of Mathematics, Mbarara University
Iran
jtumwiine@must.ac.ug


Godwin
Robert
Department of Mathematics, Mbarara University of Science and Technology,
P.O. Box 1410 Mbarara, Uganda
Department of Mathematics, Mbarara University
Iran
robertsgodwin@must.ac.ug
Bovine brucellosis
endemic equilibrium
global stability
Lyapunov function
vertical transmission
Existence and continuous dependence for fractional neutral functional differential equations
2
2
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
1

153
170


Mohammed
Abdo
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
Department of Mathematics, Dr. Babasaheb
Iran
moh_wosabi@hotmail.com


Satish
Panchal
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 India
Department of Mathematics, Dr. Babasaheb
Iran
drpanchalsk@gmail.com
Fractional differential equations
Functional differential equations
Fractional derivative and Fractional integral
Existence and continuous dependence
Fixed point theorem
An interiorpoint algorithm for $P_{ast}(kappa)$linear complementarity problem based on a new trigonometric kernel function
2
2
In this paper, an interiorpoint algorithm for $P_{ast}(kappa)$Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for largeupdate methods, which coincides with the best known complexity bound. Moreover, numerical results confirm that our new proposed kernel function is doing well in practice in comparison with some existing kernel functions in the literature.
1

171
197


Sajad
FathiHafshejani
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
Department of Mathematics, Shiraz University
Iran
s.fathi@sutech.ac.ir


Hossein
Mansouri
Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran
Department of Applied Mathematics, Shahrekord
Iran
mansouri@sci.sku.ac.ir


Mohammad Reza
Peyghami
Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran
Faculty of Mathematics, K.N. Toosi Univ.
Iran
peyghami@kntu.ac.ir
kernel function
linear complementarity problem
primaldual interior point methods
largeupdate methods