2021-09-19T02:19:21Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=473
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
Effects of ionic parameters on behavior of a skeletal muscle fiber model
Samaneh
Shahi
Hossein
Kheiri
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
2017
12
01
77
88
https://jmm.guilan.ac.ir/article_2343_1731f1b7f451e3db89d4f150c13bdc9d.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
Numerical solution of non-planar Burgers equation by Haar wavelet method
Sumana
Shesha
Achala L.
Nargund
Nagendrappa M.
Bujurke
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
2017
12
01
89
118
https://jmm.guilan.ac.ir/article_2460_de6a3c4204cdd70ae58a47355b658fa6.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response
Sambath
Muniyagounder
Ramajayam
Sahadevan
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
2017
12
01
119
136
https://jmm.guilan.ac.ir/article_2482_0f775ecfc0197e23541d4f5fbcaa278c.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
A mathematical model for treatment of bovine brucellosis in cattle population
Julius
Tumwiine
Godwin
Robert
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
2017
12
01
137
152
https://jmm.guilan.ac.ir/article_2523_c01bbe2d4b27e2285b641b5ef7880983.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
Existence and continuous dependence for fractional neutral functional differential equations
Mohammed
Abdo
Satish
Panchal
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
2017
12
01
153
170
https://jmm.guilan.ac.ir/article_2535_56ca6929d8a86326b7a2970116eeeb03.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2017
5
2
An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
Sajad
Fathi-Hafshejani
Hossein
Mansouri
Mohammad Reza
Peyghami
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 $O((1+2\kappa)\sqrt{n} \log n\log\frac{n}{\epsilon})$ 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
2017
12
01
171
197
https://jmm.guilan.ac.ir/article_2537_cf3ea063a8ab351a654ae8a859b24f8d.pdf