## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (202.070 recursos)

International Journal of Differential Equations

1. #### Modeling and Analysis of Integrated Pest Control Strategies via Impulsive 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...

2. #### Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest

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...

3. #### Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

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.

4. #### Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

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.

5. #### Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

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.

6. #### The Morbidity of Multivariable Grey Model MGM$(\mathrm 1,m)$

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.

7. #### The Morbidity of Multivariable Grey Model MGM$(\mathrm 1,m)$

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.

8. #### Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: $(m+1)$ th-Step Block Method

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...

9. #### Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: $(m+1)$ th-Step Block Method

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...

10. #### Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: $(m+1)$ th-Step Block Method

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...

11. #### Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

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.

12. #### Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

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.

13. #### Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

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.

14. #### Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

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.

15. #### Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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.

16. #### Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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.

17. #### Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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.

18. #### Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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.

19. #### Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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.

20. #### Cyclic Growth and Global Stability of Economic Dynamics of Kaldor Type in Two Dimensions

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.

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