JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2343 Research Paper Effects of ionic parameters on behavior of a skeletal muscle fiber model Effects of ionic parameters on behavior of a skeletal muscle model Shahi Samaneh Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Kheiri Hossein Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran 01 12 2017 5 2 77 88 25 07 2017 25 07 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2343.html

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
JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2460 Research Paper Numerical solution of non-planar Burgers equation by Haar wavelet method Numerical solution of non-planar Burgers equation by Haar wavelets Shesha Sumana R Bangalore University Nargund Achala L. Department of Studies in Mathematics, Karnatak University, Dharwad, India Bujurke Nagendrappa M. Department of Studies in Mathematics, Karnatak University, Dharwad, India 01 12 2017 5 2 89 118 04 10 2017 04 10 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2460.html

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
JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2482 Research Paper Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response Prey-predator model with diffusion Muniyagounder Sambath Department of Mathematics, Periyar University, Salem-636011, India Sahadevan Ramajayam Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-600005, India 01 12 2017 5 2 119 136 01 11 2017 01 11 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2482.html

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
JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2523 Research Paper A mathematical model for treatment of bovine brucellosis in cattle population Dynamics of bovine brucellosis in cattle population Tumwiine Julius Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda Robert Godwin Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda 01 12 2017 5 2 137 152 01 12 2017 01 12 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2523.html

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
JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2535 Research Paper Existence and continuous dependence for fractional neutral functional differential equations Fractional neutral functional differential equations Abdo Mohammed Salem Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India Panchal Satish Kushaba Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 India 01 12 2017 5 2 153 170 05 12 2017 05 12 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2535.html

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
JMM دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2017.2537 Research Paper An interior-point algorithm for \$P_{ast}(kappa)\$-linear complementarity problem based on a new trigonometric kernel function An interior-point algorithm for \$P_{ast}(kappa)\$-linear complementaritydots Fathi-Hafshejani Sajad Department of Mathematics, Shiraz University of Technology, Shiraz, Iran Mansouri Hossein Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran Peyghami Mohammad Reza Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran 01 12 2017 5 2 171 197 08 12 2017 08 12 2017 Copyright © 2017, دانشگاه گیلان. 2017 https://jmm.guilan.ac.ir/article_2537.html

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