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