eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
77
88
10.22124/jmm.2017.2343
2343
مقاله پژوهشی
Effects of ionic parameters on behavior of a skeletal muscle fiber model
Samaneh Shahi
samanesh7@gmail.com
1
Hossein Kheiri
h-kheiri@tabrizu.ac.ir
2
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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.
https://jmm.guilan.ac.ir/article_2343_1731f1b7f451e3db89d4f150c13bdc9d.pdf
action potential
sensitive analysis
skeletal muscle
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
89
118
10.22124/jmm.2017.2460
2460
مقاله پژوهشی
Numerical solution of non-planar Burgers equation by Haar wavelet method
Sumana Shesha
sumana.shesha@gmail.com
1
Achala L. Nargund
anargund1960@gmail.com
2
Nagendrappa M. Bujurke
bujurke@yahoo.com
3
Bangalore University
Department of Studies in Mathematics, Karnatak University, Dharwad, India
Department of Studies in Mathematics, Karnatak University, Dharwad, India
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.
https://jmm.guilan.ac.ir/article_2460_de6a3c4204cdd70ae58a47355b658fa6.pdf
Haar wavelets
non-planar Burgers equation
quasilinearization
collocation points
finite difference
cylindrical and spherical geometry
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
119
136
10.22124/jmm.2017.2482
2482
مقاله پژوهشی
Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response
Sambath Muniyagounder
sambathbu2010@gmail.com
1
Ramajayam Sahadevan
ramajayamsaha@yahoo.co.in
2
Department of Mathematics, Periyar University, Salem-636011, India
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-600005, India
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.
https://jmm.guilan.ac.ir/article_2482_0f775ecfc0197e23541d4f5fbcaa278c.pdf
stability
prey-predator
Monod-Haldane response
Hopf bifurcation
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
137
152
10.22124/jmm.2017.2523
2523
مقاله پژوهشی
A mathematical model for treatment of bovine brucellosis in cattle population
Julius Tumwiine
jtumwiine@must.ac.ug
1
Godwin Robert
robertsgodwin@must.ac.ug
2
Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda
Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda
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 $mathcal{R}_{0}1$. 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.
https://jmm.guilan.ac.ir/article_2523_c01bbe2d4b27e2285b641b5ef7880983.pdf
Bovine brucellosis
endemic equilibrium
global stability
Lyapunov function
vertical transmission
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
153
170
10.22124/jmm.2017.2535
2535
مقاله پژوهشی
Existence and continuous dependence for fractional neutral functional differential equations
Mohammed Abdo
moh_wosabi@hotmail.com
1
Satish Panchal
drpanchalsk@gmail.com
2
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 India
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.
https://jmm.guilan.ac.ir/article_2535_56ca6929d8a86326b7a2970116eeeb03.pdf
Fractional differential equations
Functional differential equations
Fractional derivative and Fractional integral
Existence and continuous dependence
Fixed point theorem
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-12-01
5
2
171
197
10.22124/jmm.2017.2537
2537
مقاله پژوهشی
An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
Sajad Fathi-Hafshejani
s.fathi@sutech.ac.ir
1
Hossein Mansouri
mansouri@sci.sku.ac.ir
2
Mohammad Reza Peyghami
peyghami@kntu.ac.ir
3
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran
Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran
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.
https://jmm.guilan.ac.ir/article_2537_cf3ea063a8ab351a654ae8a859b24f8d.pdf
kernel function
linear complementarity problem
primal-dual interior point methods
large-update methods