Qamar Din

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Verified

Qamar verified their affiliation via an institutional email.

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• Ph.D in Mathematics
• Professor (Full) at University of Poonch Rawalakot

This study investigates the dynamical behavior of a modified Brusselator model, with a particular focus on codimension-one bifurcations, including period-doubling and Neimark–Sacker bifurcations. Additionally, it examines codimension-two bifurcations associated with strong resonances such as 1:2, 1:3, and 1:4. The analysis is carried out using the...

The interplay of non-overlapping generations and cannibalism within prey populations can generate complex predator–prey relationships, significantly influencing population dynamics. This research investigates the complexities of codimension-two bifurcations in a discrete-time predator–prey model, distinguished by its inclusion of cannibalistic dyna...

This article explores the dynamic behavior of a fractional-order Schnakenberg chemical reaction model. Specifically, we conduct an analysis of codimension-two bifurcation associated with 1:2, 1:3, and 1:4 resonances. To achieve these results, we utilize the normal form method and bifurcation theory. The findings are illustrated through detailed num...

This study involves discretizing a continuous-time glycolysis model to derive its discrete-time equivalent and investigates its dynamics using normal form theory and bifurcation analysis. The discretization employs the forward Euler's scheme, and through rigorous analysis, we delve into codimension two bifurcations, with a specific focus on the 1:2...

In predator–prey interactions, the effect of fear is an important factor in building ecological communities, affecting biodiversity, and maintaining ecological balance. In this paper, we present a specific predator–prey model that incorporates the effects of fear on prey populations by focusing on non-overlapping generations. Our study aims to expl...

The purpose of this article is to determine the expressions of solutions for the following rational difference systemsΦn+1 = Φn−2Ψn / α + Φn−2 + Ψn−3, Ψn+1 = ΦnΨn−2 / β ± Φn−3 ± Ψn−2, n = 0, 1, 2, ...,where α and β are arbitrary real numbers. Furthermore, the solution’s qualitative behavior is explored, such as local and global stability, as well a...

Modelling has become an eminent tool in the study of ecological systems. Ecological modelling can help implement sustainable development, mathematical models, and system analysis that explain how ecological processes can promote the sustainable management of resources. In this paper, we also chose a four-dimensional discrete-time Lotka–Volterra eco...

This paper explores the qualitative behavior of a discrete fractional-order Brusselator model. We analyze the local dynamics of the model around its fixed point and determine its topological classification. We perform the bifurcation analysis for both codimension-one and codimension-two cases to examine the system behavior near critical parameter v...

This study investigates the dynamics of predator–prey interactions with non-overlapping generations under the influence of fear effects, a crucial factor in ecological research. We propose a novel discrete-time model that addresses limitations of previous models by explicitly incorporating fear. Our primary question is: How does fear influence the...

The occurrence of cannibalism is common in natural colonies and can substantially affect the functional relationships between predators and prey. Despite the belief that cannibalism stabilizes or destabilizes predator–prey models, its effects on prey populations are not well-understood. In this study, we propose a discrete-time prey–predator model...

In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrat...

Cyclic types of ecological dynamics have been found in several biological species of forest Lepidoptera. There are several possible reasons for this, for example, interactions with consumers, predators, plant quality index, and interactions of density-dependent type. Furthermore, interaction with consumers and plant quality index is regarded as key...

Recent studies on terrestrial vertebrates have unveiled a correlation between fear of predators and a reduction in anti-predator defenses, leading to a significant decline in prey reproduction. Given the critical importance of prey population levels, we have introduced a fear factor into a discrete-time predator–prey model to investigate its influe...

This article delves into an investigation of the dynamic behavior exhibited by a fractional order cubic autocatalator chemical reaction model. Specifically, our focus lies on exploring codimension-one bifurcations associated with period-doubling bifurcation and Neimark-Sacker bifurcation. Additionally, we undertake an analysis of codimension-two bi...

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting...

Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steady-states, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced b...

Numerous field data and experiments on the perching birds or songbirds show that the fear of predators can cause significant changes in the prey population. Fear of predatory populations increases the chances of survival of the prey population, and this can greatly reduce the reproduction of the prey population. The influence of fear has contribute...

Purpose The purpose of the present work is to develop a new wavelet method, named as Krawtchouk wavelets method, for solving both Caputo fractional and Caputo–Hadamard fractional differential equations on a semi‐infinite domain. Design/methodology/approach We have utilized the discrete Krawtchouk orthogonal polynomial for the construction of Krawt...

Taking into account an ideal mixture and a well-stirred reactor, some dynamical aspects for a 3-dimensional chaotic system are carried out. Positivity and boundedness of solutions are discussed. Equilibria are investigated and method of linearization is implemented for asymptotic behavior of system about these equilibria. Lyapunov function is const...

The present study focuses on the dynamical aspects of a discrete-time Leslie-Gower predator-prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologic...

This article deals with the study of some qualitative properties of a cubic autocatalator chemical reaction model. Particularly, we obtain a dynamically consistent cubic autocatalator discrete-time model by applying a nonstandard difference scheme. Analysis of the existence of equilibria and their stability is carried out. It is proved that a conti...

In this paper, we obtain the form of the solutions of the following rational systems of difference equations \begin{document}$ \begin{equation*} x_{n+1} = \dfrac{y_{n-1}z_{n}}{z_{n}\pm x_{n-2}}, \;y_{n+1} = \dfrac{z_{n-1}x_{n} }{x_{n}\pm y_{n-2}}, \ z_{n+1} = \dfrac{x_{n-1}y_{n}}{y_{n}\pm z_{n-2}}, \end{equation*} $\end{document} with initial value...

In this paper, we study the dynamic of the predator–prey model based on mutual interference and its effects on searching efficiency. The parametric conditions, existence, and stability for trivial and boundary equilibrium points are studied. Also, it has shown that by applying the center manifold theorem and bifurcation theory, system undergoes Nei...

In this paper, we study some dynamics concerning the interaction of budmoth and plant quality index of larch situated in the Swiss Alps. Taking into account this interaction, a two-dimensional discrete-time system is formulated and discussed. The new model is formulated with an application of Holling type III functional response for the plant quali...

In this article, a modification is proposed for the classical Nicholson–Bailey model. It is assumed that the modified model follows all axioms of Nicholson–Bailey model except that in every generation a fraction of the hosts have a safe refuge from attack of parasitoids. It is investigated that under this assumption the modified model has stable co...

The main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a system of differential algebraic equations. It is sh...

Keeping in mind the interactions between budmoths and the quality of larch trees located in the Swiss Alps (a mountain range in Switzerland), a discrete-time model is proposed and studied. The novel model is proposed with implementation of a nonlinear functional response that incorporates plant quality. The proposed functional response is validated...

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form...

PurposeThe main aim of the paper is to introduce the shifted fractional-order Gegenbauer wavelets (SFGWs) and the development of a method for solving fractional nonlinear initial and boundary value problems on a semi-infinite domain.Design/methodology/approachThe proposed method is the combination of SFGWs and parametric iteration method. We have d...

In order to see the dynamics of prey-predator interaction, differential or difference equations are frequently used for modeling of such interactions. In present manuscript, we explore some qualitative aspects of two-dimensional ratio-dependent predator-prey model. Taking into account the non-overlapping generations for class of predator-prey syste...

The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by...

Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of the...

The interaction between prey and predator is well--known within natural ecosystems. Due to their multifariousness and strong link population dynamics, predators contain distinct features of ecological communities. Keeping in view the Nicholson-Bailey framework for host-parasitoid interaction, a discrete-time predator-prey system is formulated and s...

Schnakenberg model is a system showing sustained oscillations for a simple model of glycolysis in which a metabolic process that converts glucose to provide energy for metabolism. Euler approximation is implemented to obtain discrete version of Schnakenberg model. It is proved that discrete-time system via Euler approximation undergoes Neimark–Sack...

This paper is related to some dynamical aspects of a class of predator-prey interactions incorporating cannibalism and Allee effects for non-overlapping generations. Cannibalism has been frequently observed in natural populations, and it has an ability to alter the functional response concerning prey-predator interactions. On the other hand, from d...

The positive connection between the total individual fitness and population density is called the demographic Allee effect. A demographic Allee effect with a critical population size or density is strong Allee effect. In this paper, discrete counterpart of Bazykin–Berezovskaya predator–prey model is introduced with strong Allee effects. The steady...

Bifurcation theory (center manifold and Ljapunov–Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discre...

Cannibalism is ubiquitous in natural communities and has the tendency to change the functional connection among prey-predator interactions. Keeping in view the inclusion of prey cannibalism, a novel discrete nonlinear predator-prey model is proposed. Asymptotic stability is carried out around biologically feasible equilibria of proposed model. Cent...

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existe...

In this paper we consider a system of second order rational difference equations. We mainly discuss the boundedness and persistence, existence of fixed point, and uniqueness of positive fixed point, local and global behavior of positive fixed point and rate of convergence of every positive solution of the system under discussion. It will be show...

Intermediate filaments are the mechanical ropes for both cytoskeleton and nucleoskeleton of the cell which provide tensile force to these skeletons. In providing the mechanical support to the cell, they are likely to buckle. We used conventional Euler buckling model to find the critical buckling force under different boundary conditions which they...

The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability...

Parasites play vital role in dynamics of predator–prey interaction and regulating bio-diversity. We study qualitative behavior of two 3-dimensional discrete-time predator–prey-parasite models. Bifurcation analysis and chaos control are discussed by taking into account the study of an eco–epidemiological model of pelicans at risk in the Salton Sea....

Abstract We investigate the dynamical behavior of a modified Leslie–Gower prey–predator model with harvesting in prey population. In order to explore rich dynamics of the model, Euler approximation is implemented to obtain a discrete-time modified Leslie–Gower model. Existence of equilibria and their local asymptotic stabilities are carried out. Fu...

The aim of this article is to study the local stability of equilibria, investigation related to the parametric conditions for transcritical bifurcation, period-doubling bifurcation and Neimark-Sacker bifurcation of the following second-order difference equation x n+1 = αx n + βx n−1 exp(−σx n−1) where the initial conditions x −1 , x 0 are the arbit...

Predator-prey models are basic of bio and ecosystem. Different living things decompose, evolve and change their lives and struggle for their survival. Depending on their specific settings of application they can take forms of resource-consumer, plant-herbivore, parasite-host, tumor cells (virus)-immune system, susceptible-infectious interactions et...

The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the dynamical consistency for co...

We investigate the dynamics of two‐dimensional discrete‐time model of leaf quality and larch budmoth interaction with Ricker equation. More precisely, the qualitative behavior of larch budmoth model is discussed in which the effect of food source upon the moth population is through intrinsic growth rate. We find the parametric conditions for local...

This paper deals with the qualitative study of a discrete-time prey-predator model with Holling type-II response. Particularly, we obtained a dynamically consistent prey-predator discrete-time model by applying a nonstandard difference scheme. We explore the novel explicate parametric conditions for the local stability of positive equilibrium point...

This article deals with qualitative analysis of a smoking model and provides parametric conditions for controlling diseases under the influence of smoking. The model is obtained by taking into account a novel uptake function, which relates the incidence of potential smoker with occasional smoker, of harmonic mean type for the potential and occasion...

The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the a...

Abstract The interaction between plants and herbivores plays a vital role for understanding community dynamics and ecosystem function given that they are the critical link between primary production and food webs. This paper deals with the qualitative nature of two discrete-time plant–herbivore models. In both discrete-time models, function for pla...

In this work, our main goal is to study a new wave behavior of the nonlinear system associated with ionic wave equations under the influence of the ponderomotive force caused by a nonlinear force experienced by a charged particle in an inhomogeneous oscillating electromagnetic field due to high-frequency field. Another variation in the modified exp...

The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey-predator model is investigated. Particularly, we examine the boundedness as well as existence and uniqueness of positive steady-state and stability an...

The dynamical behavior of the predator-prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementation of nonlinear saturated incidence rate and piecewise constant argument method of differential equations, a three-dimensional discrete-tim...

In this paper, we discuss the qualitative behavior of a four-dimensional discrete-time predator–prey model with parasites. We investigate existence and uniqueness of positive steady state and find parametric conditions for local asymptotic stability of positive equilibrium point of given system. It is also proved that the system undergoes Neimark–S...

The aim of this paper is to investigate the qualitative behavior of a higher-order nonautonomous rational difference equation with periodic coefficients. Particularly, our investigation gives some answers to two open problems proposed by Camouzis and Ladas in their monograph (Dynamics of third order rational difference equations with open problems...

This article deals with the dynamical analysis of discrete-time Brusselator models. Euler’s forward and nonstandard difference schemes are implemented for discretization of Brusselator system. We investigate the local dynamics related to equilibria of both discrete-time models. Furthermore, with the help of bifurcation theory and center manifold th...

Purpose The purpose of this paper is to propose a method for solving nonlinear fractional partial differential equations on the semi-infinite domain and to get better and more accurate results. Design/methodology/approach The authors proposed a method by using the Chebyshev wavelets in conjunction with differential quadrature technique. The oper...

Basically enzymes are biological catalysts that increase the speed of a chemical reaction without undergoing any permanent chemical change. With the application of Euler’s forward scheme, a discrete-time enzyme model is presented. Further investigation related to its qualitative behaviour revealed that discrete-time model shows rich dynamics as com...

In this paper, dynamics of a two-dimensional Fitzhugh-Nagumo model is discussed. The discrete-time model is obtained with the implementation of forward Euler's scheme. We present the parametric conditions for local asymptotic stability of steady-states. It is shown that the two-dimensional discrete-time model undergoes period-doubling bifurca-tion...

We study qualitative behavior of a modified prey–predator model by introducing density-dependent per capita growth rates and a Holling type II functional response. Positivity of solutions, boundedness and local asymptotic stability of equilibria were investigated for continuous type of the prey–predator system. In order to discuss the rich dynamics...

We study the comprehensive dynamics of a density-dependent host–parasitoid system with the Hassell growth function for the host population. Particularly, we investigate the dynamical properties related to boundedness, local asymptotic stability of boundary equilibrium, existence and uniqueness of positive equilibrium point and global asymptotic sta...

In this paper, a discrete-time prey-predator model with Allee effect is proposed. The parametric conditions for local asymptotic stability of steady-states are investigated. Moreover, we discuss the existence and directions of period-doubling and Neimark-Sacker bifurcations with the of help center manifold theorem and bifurcation theory. In order t...

In this paper, a new density‐dependent host–parasitoid model is proposed. The modification is based on density‐dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium...

In this paper, we investigate the complex dynamics of three-dimensional Ricker-type discrete-time competition model. We discuss the existence and uniqueness, and find parametric conditions for local asymptotic stability of positive fixed point of this model. It is also proved that the system undergoes Neimark–Sacker (NS) and period-doubling bifurca...

In this paper, the qualitative behavior of two discrete-time glycolysis models is discussed. The discrete-time models are obtained by implementing forward Euler’s scheme and nonstandard finite difference method. The parametric conditions for local asymptotic stability of positive steady-states are investigated. Moreover, we discuss the existence an...

In this paper, we give some new refinements of Hermite-Hadamard inequality for co-ordinated convex function. These refinements provide us better estimation as compare to the earlier established refinements of Hadamard’s inequality.

In this paper, the qualitative behavior of discrete-time models related to chlorine dioxide-iodine-malonic acid reaction is discussed. The discrete-time models are obtained by implementing forward Euler's scheme followed by nonstandard difference scheme. The parametric conditions for local asymptotic stability of positive steady-state are investiga...

In this paper, we study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equations with initial conditions and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness, persistence and stability analysis of a second-order fuzzy rational differenc...

This work is related to dynamics of a second-order rational difference equation. We investigate the parametric conditions for local asymptotic stability of equilibria. Center manifold theorem and bifurcation theory are implemented to discuss the parametric conditions for existence and direction of period-doubling bifurcation and pitchfork bifurcati...

This article deals with the study of some qualitative properties of a discrete-time mosquito Model. It is shown that there exists period-doubling bifurcation for wide range of bifurcation parameter for the unique positive steady-state of given system. In order to control the bifurcation we introduced a feedback strategy. For further confirmation of...

We discuss qualitative behavior of a discrete-time density-dependent predator-prey model. More precisely, we discuss the existence and uniqueness of positive steady-state, permanence, local and global behavior of unique positive equilibrium point and the rate of convergence of positive solutions that converge to the unique positive equilibrium poin...

This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive e...

We investigate the qualitative behavior of a host-parasitoid model with a strong Allee effect on the host. More precisely, we discuss the boundedness, existence and uniqueness of positive equilibrium, local asymptotic stability of positive equilibrium and existence of Neimark–Sacker bifurcation for the given system by using bifurcation theory. In o...

We investigate qualitative behaviour of a density-dependent discrete-time host-parasitoid model. Particularly, we study boundedness of solutions, existence and uniqueness of positive steady-state, local and global asymptotic stability of the unique positive equilibrium point and rate of convergence of modified host-parasitoid model.Moreover, it is...

We investigate the complex behavior and chaos control in a discrete-time prey-predator model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete-time prey-predator system with predator partially dependent on prey and investigate the boundedness, existence and uniqueness of positive equilibrium and bifurcation analysis o...

In this paper, we propose a discrete-time host-pathogen model and study its qualitative behavior. The model is for the spread of an infectious disease with constant mortality rate of hosts. Moreover, the time-step is equal to the duration of the infectious phase, and the host mortality is taken at some constant rate d >0. This two-dimensional discr...

We investigate the complex behaviour of a modified Nicholson–Bailey model. The modification is proposed by Hassel and Varley taking into account that interaction between parasitoids is taken in such a way that the searching area per parasitoid is inversely proportional to the m-th power of the population density of parasitoids. Under certain parame...

We study some qualitative behaviour of a modified discrete-time host–parasitoid model. Modification of classical Nicholson–Bailey model is considered by introducing Pennycuick growth function for the host population. Furthermore, the existence and uniqueness of positive equilibrium point of proposed system is investigated. We prove that the positiv...

In this paper, we introduce a fractional order model of vector-host disease. The stability of disease free and endemic equilibria are also studied. We provide a general procedure for implementing the Adam-Bashforth predictor corrector method on biological system and it is utilized for solving the proposed model. Numerical simulations are pre- sente...

This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes in...

In this paper our aim is to give refinements of Jensen’s type inequalities for the convex function defined on the co-ordinates of the bidimensional interval in the plane.

In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease-free equilibrium and the endemic equilibrium. Furthermore, by using comparison method, we obtain the global stability of these equilibrium points under certain parametric conditi...

We study the qualitative behavior of a smoking model in which the population is divided into five classes, that is, non-smokers, smokers, people who temporarily quit smoking, people who permanently quit smoking, and people who are associated with illness due to smoking. The global asymptotic stability of the unique positive equilibrium point is pre...