Abstract: Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work. PubDate: Thu, 12 Apr 2018 00:00:00 +000

Abstract: An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on. PubDate: Sun, 01 Apr 2018 00:00:00 +000

Abstract: We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination. PubDate: Thu, 15 Mar 2018 00:00:00 +000

Abstract: We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number and the CTL immune response reproduction number . The stability of the last equilibrium depends on and as well as time delay in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when passes through a certain critical value. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: We prove some uniqueness results for the solution of two kinds of Dirichlet boundary value problems for second- and fourth-order linear elliptic differential equations with discontinuous coefficients in polyhedral angles, in weighted Sobolev spaces. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: We consider the following nonlinear parabolic equation: , where and the exponent of nonlinearity are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: It is known that power series expansion of certain functions such as diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of that is convergent for all . The convergent series is a sum of the Taylor series of and a complementary series that cancels the divergence of the Taylor series for . The method is general and can be applied to other functions known to have finite radius of convergence, such as . A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed. PubDate: Tue, 13 Feb 2018 00:00:00 +000

Abstract: We propose a generalized virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the distributed delays describe (i) the time needed for infected cells to produce new virions and (ii) the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modeled by general incidence functions for both modes. Furthermore, the qualitative analysis of the model is rigorously established and many known viral infection models with discrete and distributed delays are extended and improved. PubDate: Thu, 01 Feb 2018 00:00:00 +000

Abstract: The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the treatment at this stage, we also consider two types of treatment: interferon- (IFN) and nucleoside analogues (NAs). To find the best strategy to use this treatment, an optimal control approach is developed to find the possibility of having a functional cure to HBV. PubDate: Thu, 01 Feb 2018 00:00:00 +000

Abstract: We discuss the existence of global solutions to the magnetohydrodynamics (MHD) equations, where the effects of finite Larmor radius corrections are taken into account. Unlike the usual MHD, the pressure is a tensor and it depends on not only the density but also the magnetic field. We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate. PubDate: Sun, 28 Jan 2018 00:00:00 +000

Abstract: In this article, the linearization problem of fifth-order ordinary differential equation is presented by using the generalized Sundman transformation. The necessary and sufficient conditions which allow the nonlinear fifth-order ordinary differential equation to be transformed to the simplest linear equation are found. There is only one case in the part of sufficient conditions which is surprisingly less than the number of cases in the same part for order 2, 3, and 4. Moreover, the derivations of the explicit forms for the linearizing transformation are exhibited. Examples for the main results are included. PubDate: Tue, 02 Jan 2018 00:00:00 +000

Abstract: We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen. PubDate: Mon, 01 Jan 2018 08:54:26 +000

Abstract: Bioeconomic modeling of the exploitation of biological resources such as fisheries has gained importance in recent years. In this work we propose to define and study a bioeconomic equilibrium model for two fishermen who catch three species taking into consideration the fact that the prices of fish populations vary according to the quantity harvested; these species compete with each other for space or food; the natural growth of each species is modeled using a logistic law. The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is the preservation of the biodiversity. The existence of the steady states and their stability are studied using eigenvalue analysis. The problem of determining the equilibrium point that maximizes the profit of each fisherman leads to Nash equilibrium problem; to solve this problem we transform it into a linear complementarity problem (LCP); then we prove that the obtained problem (LCP) admits a unique solution that represents the Nash equilibrium point of our problem. We close our paper with some numerical simulations. PubDate: Tue, 26 Dec 2017 00:00:00 +000

Abstract: We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results. PubDate: Thu, 07 Dec 2017 00:00:00 +000

Abstract: The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM). Established in the late 1950s, IPM is a pest management paradigm that involves the combination of different pest control methods in ways that complement one another, so as to reduce excessive use of pesticides and minimize environmental impact. Since the introduction of the IPM concept, a rich set of mathematical models has emerged, and the present work discusses the development in this area in recent years. Furthermore, a comprehensive parametric study of an IPM-based impulsive control scheme is carried out via path-following techniques. The analysis addresses practical questions, such as how to determine the parameter values of the system yielding an optimal pest control, in terms of operation costs and environmental damage. The numerical study concludes with an exploration of the dynamical features of the impulsive model, which reveals the presence of codimension-1 bifurcations of limit cycles, hysteretic effects, and period-doubling cascades, which is a precursor to the onset of chaos. PubDate: Sun, 03 Dec 2017 00:00:00 +000

Abstract: We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings. PubDate: Thu, 09 Nov 2017 07:04:27 +000

Abstract: This paper proposes the morbidity of the multivariable grey prediction MGM model. Based on the morbidity of the differential equations, properties of matrix, and Gerschgorin Panel Theorem, we analyze the factors that affect the morbidity of the multivariable grey model and give a criterion to justify the morbidity of MGM. Finally, an example is presented to illustrate the practicality of our results. PubDate: Sun, 05 Nov 2017 07:24:28 +000

Abstract: Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A -step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the -step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium. PubDate: Sun, 29 Oct 2017 00:00:00 +000

Abstract: This paper studies the behavior of a predator-prey model with switching and stage-structure for predator. Bounded positive solution, equilibria, and stabilities are determined for the system of delay differential equation. By choosing the delay as a bifurcation parameter, it is shown that the positive equilibrium can be destabilized through a Hopf bifurcation. Some numerical simulations are also given to illustrate our results. PubDate: Wed, 27 Sep 2017 00:00:00 +000

Abstract: We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results. PubDate: Sun, 27 Aug 2017 00:00:00 +000

Abstract: This article proposes nonlinear economic dynamics continuous in two dimensions of Kaldor type, the saving rate and the investment rate, which are functions of ecological origin verifying the nonwasting properties of the resources and economic assumption of Kaldor. The important results of this study contain the notions of bounded solutions, the existence of an attractive set, local and global stability of equilibrium, the system permanence, and the existence of a limit cycle. PubDate: Sun, 02 Jul 2017 07:36:05 +000

Abstract: A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given. PubDate: Wed, 14 Jun 2017 00:00:00 +000

Abstract: An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations. PubDate: Tue, 13 Jun 2017 00:00:00 +000

Abstract: The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments. PubDate: Sun, 11 Jun 2017 09:20:09 +000

Abstract: In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example. PubDate: Sun, 30 Apr 2017 06:19:33 +000

Abstract: We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters and . We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system. PubDate: Mon, 24 Apr 2017 00:00:00 +000

Abstract: This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering. PubDate: Mon, 13 Mar 2017 07:50:09 +000

Abstract: We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients. PubDate: Mon, 27 Feb 2017 00:00:00 +000

Abstract: For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state to an neighbourhood of the target state at time under the assumption that the nonlinear function is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained. PubDate: Thu, 23 Feb 2017 00:00:00 +000

Abstract: In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods. PubDate: Wed, 08 Feb 2017 00:00:00 +000