Recursos de colección
Project Euclid (Hosted at Cornell University Library) (202.070 recursos)
International Journal of Differential Equations
International Journal of Differential Equations
Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan
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...
Agmour, Imane; Bentounsi, Meriem; Achtaich, Naceur; El Foutayeni, Youssef
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...
Acosta, A.; García, P.; Leiva, H.; Merlitti, A.
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.
Ávila-Vales, Eric; Rivero-Esquivel, Erika; García-Almeida, Gerardo Emilio
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form $Sf(I)$ , 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.
Ávila-Vales, Eric; Rivero-Esquivel, Erika; García-Almeida, Gerardo Emilio
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form $Sf(I)$ , 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.
Wang, Haixia; Zhao, Lingdi; Hu, Mingzhao
This paper proposes the morbidity of the multivariable grey prediction MGM$(\mathrm 1,m)$ 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$(\mathrm 1,m)$. Finally, an example is presented to illustrate the practicality of our results.
Wang, Haixia; Zhao, Lingdi; Hu, Mingzhao
This paper proposes the morbidity of the multivariable grey prediction MGM$(\mathrm 1,m)$ 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$(\mathrm 1,m)$. Finally, an example is presented to illustrate the practicality of our results.
Adeyeye, Oluwaseun; Omar, Zurni
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 $(m+\mathrm{1})\mathrm{t}\mathrm{h}$ -step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where $m$ is the order of the differential equation under consideration. The schemes obtained were...
Adeyeye, Oluwaseun; Omar, Zurni
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 $(m+\mathrm{1})\mathrm{t}\mathrm{h}$ -step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where $m$ is the order of the differential equation under consideration. The schemes obtained were...
Adeyeye, Oluwaseun; Omar, Zurni
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 $(m+\mathrm{1})\mathrm{t}\mathrm{h}$ -step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where $m$ is the order of the differential equation under consideration. The schemes obtained were...
Suebcharoen, T.
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.
Suebcharoen, T.
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.
Suebcharoen, T.
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.
Suebcharoen, T.
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.
Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
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.
Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
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.
Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
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.
Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
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.
Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
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.
Nindjin, Aka Fulgence; N’Guessan, Albin Tetchi; Okou, Hypolithe; Tia, Kessé Thiban
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.