University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
Effects of ionic parameters on behavior of a skeletal muscle fiber model
77
88
EN
Samaneh
Shahi
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
samanesh7@gmail.com
Hossein
Kheiri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
h-kheiri@tabrizu.ac.ir
10.22124/jmm.2017.2343
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 Hodgkin-Huxley 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, Na-K 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.
action potential,sensitive analysis,skeletal muscle
https://jmm.guilan.ac.ir/article_2343.html
https://jmm.guilan.ac.ir/article_2343_1731f1b7f451e3db89d4f150c13bdc9d.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
Numerical solution of non-planar Burgers equation by Haar wavelet method
89
118
EN
Sumana
R
Shesha
Bangalore University
sumana.shesha@gmail.com
Achala L.
Nargund
Department of Studies in Mathematics, Karnatak University, Dharwad, India
anargund1960@gmail.com
Nagendrappa M.
Bujurke
Department of Studies in Mathematics, Karnatak University, Dharwad, India
bujurke@yahoo.com
10.22124/jmm.2017.2460
In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar 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 non-planar and nonlinear geometry on shock existence. We observe that non-planar shock structures are different from planar ones. It is of interest to find that Haar wavelets enable to predict the shock structure accurately.
Haar wavelets,non-planar Burgers equation,quasilinearization,collocation points,finite difference,cylindrical and spherical geometry
https://jmm.guilan.ac.ir/article_2460.html
https://jmm.guilan.ac.ir/article_2460_de6a3c4204cdd70ae58a47355b658fa6.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response
119
136
EN
Sambath
Muniyagounder
Department of Mathematics, Periyar University, Salem-636011, India
sambathbu2010@gmail.com
Ramajayam
Sahadevan
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-600005, India
ramajayamsaha@yahoo.co.in
10.22124/jmm.2017.2482
In this paper, we have studied the diffusive predator-prey model with Monod-Haldane 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 non-homogeneous 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.
Stability,prey-predator,Monod-Haldane response,Hopf bifurcation
https://jmm.guilan.ac.ir/article_2482.html
https://jmm.guilan.ac.ir/article_2482_0f775ecfc0197e23541d4f5fbcaa278c.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
A mathematical model for treatment of bovine brucellosis in cattle population
137
152
EN
Julius
Tumwiine
0000-0002-7904-6698
Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda
jtumwiine@must.ac.ug
Godwin
Robert
Department of Mathematics, Mbarara University of Science and Technology,
P.O. Box 1410 Mbarara, Uganda
robertsgodwin@must.ac.ug
10.22124/jmm.2017.2523
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 disease-free 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.
Bovine brucellosis,endemic equilibrium,global Stability,Lyapunov function,vertical transmission
https://jmm.guilan.ac.ir/article_2523.html
https://jmm.guilan.ac.ir/article_2523_c01bbe2d4b27e2285b641b5ef7880983.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
Existence and continuous dependence for fractional neutral functional differential equations
153
170
EN
Mohammed
Salem
Abdo
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
moh_wosabi@hotmail.com
Satish
Kushaba
Panchal
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 India
drpanchalsk@gmail.com
10.22124/jmm.2017.2535
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.
Fractional differential equations,Functional differential equations,Fractional derivative and Fractional integral,Existence and continuous dependence,Fixed point theorem
https://jmm.guilan.ac.ir/article_2535.html
https://jmm.guilan.ac.ir/article_2535_56ca6929d8a86326b7a2970116eeeb03.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
2
2017
12
01
An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
171
197
EN
Sajad
Fathi-Hafshejani
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
s.fathi@sutech.ac.ir
Hossein
Mansouri
Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran
mansouri@sci.sku.ac.ir
Mohammad Reza
Peyghami
Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran
peyghami@kntu.ac.ir
10.22124/jmm.2017.2537
In this paper, an interior-point 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 large-update 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.
kernel function,linear complementarity problem,primal-dual interior point methods,large-update methods
https://jmm.guilan.ac.ir/article_2537.html
https://jmm.guilan.ac.ir/article_2537_cf3ea063a8ab351a654ae8a859b24f8d.pdf