R. Khoshsiar Ghaziani

Shahrekord University | SKU · Department of Applied Mathematics

Studying convection–diffusion problems of delayed type in physics helps us to understand transport phenomena and has practical applications in various fields. The mathematical analysis of this model has practical applications in various fields, such as flow dynamics, material science, and environmental modeling. In this paper, the theory of reprodu...

This paper focuses on the different bifurcations of fixed points of a delayed discrete neural network model analytically and numerically. The conditions and critical values of different bifurcations including the pitchfork, flip, Neimark–Sacker, and flip–Neimark–Sacker are analyzed. By using the critical coefficients, the structure for each bifurca...

The present paper investigates the critical normal form coefficients for the one-parameter and two-parameter bifurcations of a two-dimensional discrete-time ratio-dependence predator–prey model. The discrete-time ratio-dependence predator–prey model exhibits the period-doubling, Neimark-Sacker, and strong resonance bifurcations. Based on the critic...

The aim of this paper is to introduce a two-dimensional discrete-time chemical model, identify its fixed points, as well as investigate one- and two-parameter bifurcations. Numerical normal forms are used in bifurcation analysis. For this model, the Neimark–Sacker and strong resonance bifurcations are observed. Based on the critical normal form coe...

A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one‐parameter and two‐parameter bifurcations. The discrete‐time prey–predator model exhibits a variety of local bifurcations such as period‐doubling, Neimark–Sacker,...

This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically, and numerically. The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method. For this model, a number of...

In this paper, we present two new projection methods based on the Hessenberg process to compute the approximate solutions of Sylvester tensor equation with low-rank right-hand side. These methods project the problem into an approximate subspace with small dimension, and then, the reduced problem is solved by applying a recursive blocked algorithm....

This paper deals with a predator-prey model and a modified version consisting of a resource-consumer with two consumer species. We analyze the stability of equilibria and for the interior equilibrium, we show that the system undergoes some generic bifurcations such as fold, Hopf and Hopf-zero bifurcations. We characterize these bifurcations by the...

In this paper, we investigate the dynamical behavior of a modified May–Holling–Tanner predator–prey model by considering the Allee effect in the prey and alternative food sources for the predator. The model is analyzed theoretically as well as numerically to determine all local codimension one and two bifurcations. Using the local parametrization m...

This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenar...

This paper studies the dynamical behavior of a Kaldor model of business cycle with discrete-time analytically and numerically. The conditions and the critical coefficients for the flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. By using the critical coefficients, the bifurcation scenarios are determined for...

In this paper, we consider a Hastings–Powell type model, which consists of a three-species food chain model with fear effect. For more realistic formulation, we incorporated two time delays into the model, one for prey density another for the gestation of the middle and top predator populations. By choosing time delays as the bifurcation parameters...

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating f...

In this paper, bifurcation analysis of a three-dimensional discrete game model is provided. Possible codimension-one (codim-1) and codimension-two (codim-2) bifurcations of this model and its iterations are investigated under variation of one and two parameters, respectively. For each bifurcation, normal form coefficients are calculated through red...

This work is devoted to study of the stability analysis of generalized fractional nonlinear system including the regularized Prabhakar derivative. We present several criteria for the generalized Mittag-Leffler stability and the asymptotic stability of this system by using the Lyapunov direct method. Further, we provide two test cases to illustrate...

In this work, we investigate the asymptotic stability analysis for two classes of nonlinear fractional systems with the regularized Prabhakar derivative. The stability analysis of the neutral and integro-differential nonlinear fractional systems are studied by assessing the eigenvalues of associated matrix and applying conditions on the nonlinear p...

In this study, we present an efficient computational method for finding approximate solution of the multi term time‐fractional diffusion equation. The approximate solution is presented in the form of a finite series in a reproducing kernel Hilbert space. The convergence of proposed method is studied under some hypothesis which provides the theoreti...

This paper deals with the stability and bifurcation of equilibria in a new chaotic fractional-order system in the sense of the Caputo fractional derivative with the chaos entanglement function. We derive conditions under which the system undergoes a Hopf bifurcation and obtain critical parameter value in the Hopf bifurcation. Moreover, the linear f...

In this paper, we studied the stabilization of nonlinear regularized Prabhakar fractional dynamical systems without and with time delay. We establish a Lyapunov stabiliy theorem for these systems and study the asymptotic stability of these systems without design a positive definite function V (without considering the fractional derivative of functi...

In this paper, we investigate the dynamical complexities of a predator-prey model with Holling type IV functional response, which describes interaction between two populations of prey and predator. We perform a bifurcation analysis of this model analytically and numerically. Our bifurcation analysis indicates that the system exhibits numerous types...

In this article, in view of the Dirichlet boundary conditions for a fractional differential equation of distributed order, we get a Lyapunov-type inequality for it. Moreover, we use this inequality to drive out a criteria for disconjugacy of zeros of the fractional differential equations.

In this article, we introduce the fractional-order T system and consider the stability of its equilibria. We investigate chaos control of fractional-order T system by means of Lyapunov stability. Further, to reveal complex behaviors of the system, numerical simulations are presented.

In this paper, we propose a numerical method to solve differential equations with generalized fractional derivative by transforming the original system into a system of ordinary differential equations of the first order. Further, we employ numerical simulation to reveal Hopf bifurcation of a system derived from the Lorenz system.

We perform a bifurcation analysis of a predator-prey model with Holling functional response. The analysis is carried out both analytically and numerically. We use dynamical toolbox MATCONT to perform numerical bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous types of bifurcation phenomena, including fo...

In this paper, we study the bifurcation and stability of a ratio-dependent predator-prey model with nonconstant predator harvesting rate. The analysis is carried out both analytically and numerically. We determine stability and dynamical behaviours of the equilibria of this system and characterize codimension 1 and codimension 2 bifurcations of the...

This article is devoted to the study of a fractional nonlinear system of differential equations including the Prabhakar fractional derivative. We present some new Lyapunov-type inequalities for this system and consider some special cases of the system .

This study develops and analyzes preconditioned Krylov subspace methods for solving discretization of the time-independent space-fractional models. First we apply a shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we apply two preconditioned iterative methods, namely, th...

This paper reports bursting behavior and related bifurcations in a fractional order FitzHugh-Nagumo neuron model, by adding sub fast-slow system. We classify different bursters of the system consisting fold/Hopf via a fold/fold hysteresis loop, homoclinic/homolininc cycle-cycle, fold/homoclinic, homoclinic/Hopf via homoclinic/fold hysteresis loop....

In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann-Liouville derivatives. In particular, we derive conditions for F -stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.

We introduce a fractional type Black-Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black-Scholes equations in terms of the generalized Mittag-Leffler functions.

In this paper we introduce the reproducing kernel method to solve a class of variational problems (VPs) depending on indefinite integrals. We discuss an analysis of convergence and error for the proposed method. Some test examples are presented to demonstrate the validity and applicability of method. The results of numerical examples indicate that...

In this paper, we present iterative and non-iterative methods for the solution of nonlinear optimal con- trol problems (NOCPs) and address the sufficient conditions for uniqueness of solution. We also study convergence properties of the given techniques. The approximate solutions are calculated in the form of a convergent series with easily comput...

In this paper, approximate solutions to a class of fractional differential equations with delay are presented by using a semi-analytical approach in Hilbert function space. Further, the uniqueness of the solution is proved in the space of real-valued continuous functions, as well as the existence of the solution is proved in Hilbert function space....

In this paper, we introduce a fractional order Leslie–Gower prey–predator model, which describes interaction between two populations of prey and predator. We determine stability and dynamical behaviors of the equilibria of this system. The dynamical behaviors consist of quasi-periodic and limit cycles. Further by numerical solution of the fractiona...

This paper investigates the dynamics and stability properties of a so-called planar truncated normal form map. This kind of map is widely used in the applied context, especially in normal form coefficients of n-dimensional maps. We determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the system....

This paper considers a Volterra’s population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solutio...

This paper investigates the dynamics and stability properties of a discrete-time Lotka-Volterra type system. We first analyze stability of the fixed points and the existence of local bifurcations. Our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic...

This paper investigates the dynamics and stability properties of a discrete-time Lotka-Volterra type system which was introduced in [7]. We first analyze stability of the fixed points and the existence of local bifurcations. Our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbe...

In this paper, we present an analytical method to solve systems of the mixed Volterra–Fredholm integral equations (VFIEs) of the second kind. By using the so called ħħ-curves, we determine the convergence parameter ħħ, which plays a key role to control convergence of approximation solution series. Further, we show that the homotopy perturbation met...

We perform a bifurcation analysis of a discrete predator–prey model with Holling functional response. We summarize stability conditions for the three kinds of fixed points of the map, further called F1,F2F1,F2 and F3F3 and collect complete information on this in a single scheme. In the case of F2F2 we also compute the critical normal form coefficie...

This paper explores the views and expectations of children regarding their school environments and has constructed a framework for the school design process based on children's information and reflections. The research objectives required analyzing secondary data, as well as qualitative and quantitative empirical studies—each one leading to the nex...

The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points (flip and Neimark-Sacker), and so es...

As an alternative to symbolic differentiation (SD) and finite differences (FD) for computing partial derivatives, we have implemented algorithmic differentiation (AD) techniques into the Matlab bifurcation software Cl_MatcontM, http://sourceforge.net/projects/matcont, where we need to compute derivatives of an iterated map, with respect to state va...

We present new or improved methods to continue heteroclinic and homoclinic orbits to fixed points in iterated maps and to compute their fold bifurcation curves, corresponding to the tangency of the invariant manifolds. The proposed methods are applicable to general n-dimensional maps and are implemented in matlab. They are based on the continuation...

The school environment affects pupils' health, work, leisure and emotions. On average, children spend around 6 hours a day and over 1000 hours a year in school. They are constantly interacting with the physical environment of their schools. However, in a review of numerous publications on educational theory and spaces, the quality of the school env...

We consider a discrete map proposed by M. Kopel that models a nonlinear Cournot duopoly consisting of a market structure between the two opposite cases of monopoly and competition. The stability of the fixed points of the discrete dynamical system is analyzed. Synchronization of two dynamics parameters of the Cournot duopoly is considered in the co...

Dynamical systems theory provides mathematical models for systems which evolve in time according to a rule, originally expressed in analytical form as a system of equations. Discrete-time dynamical systems defined by an iterated map depending on control parameters, \begin{equation} \label{Map:g} g(x,\alpha) := f^{(J)}(x,\alpha)= \underbrace{f(f(f(\...

We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a MATLAB toolbox for continuation and bifurcation analysis of dynamical systems. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, det...

We study the long-term dynamics of a two-dimensional stage structured population model for the Barents Sea cod stock with nonlinear cannibalism terms introduced by Wikan and Eide (2004). The model is represented by a two-dimensional system of difference equations for two stages of population. Following Wikan and Eide, we consider three special case...

Previous studies have shown that oesophageal and gastric cancers are the most common causes of cancer death in the Golestan Province, Iran. In 2001, we established Atrak Clinic, a referral clinic for gastrointestinal (GI) diseases in Gonbad, the major city of eastern Golestan, which has permitted, for the first time in this region, endoscopic local...

We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a matlab toolbox for continuation and bifurcation analysis of dynamical systems. This includes the numerical continuation of fixed points of iterates of the map with one control pa- rameter, d...

In this paper, an application of homotopy perturbation method is applied to finding the solutions of a generalized fifth order KdV (gfKdV) equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Thei...