Advances in Difference Equations

http://www.advancesindifferenceequations.com/

List of Papers (Total 3,023)

Dynamics of a delayed SEIQ epidemic model

In this work we consider an epidemic model that contains four species susceptible, exposed, infected and quarantined. With this model, first we find a feasible region which is invariant and where the solutions of our model are positive. Then the persistence of the model and sufficient conditions associated with extinction of infection population are discussed. To show that the...

Permanence, stability, and coexistence of a diffusive predator–prey model with modified Leslie–Gower and B–D functional response

This paper investigates a diffusive predator–prey system with modified Leslie–Gower and B–D (Beddington–DeAngelis) schemes. Firstly, we discuss stability analysis of the equilibrium for a corresponding ODE system. Secondly, we prove that the system is permanent by the comparison argument of parabolic equations. Thirdly, sufficient conditions for the global asymptotic stability of...

Strongly damped wave equations with Stepanov type nonlinear forcing term

In this paper we investigate the existence and uniqueness of weighted pseudo almost automorphic mild solution for a class of strongly damped wave equations where the semilinear forcing term is a Stepanov weighted pseudo almost automorphic function.

Dynamic output feedback control based on virtual feedback control law for planar switched nonlinear systems with time-varying delays and multiple subsystems

This paper addresses the dynamic output feedback control problem for a class of discrete-time planar switched nonlinear systems with time-varying delays and multiple subsystems. First, the virtual state feedback control law is designed based on adding a power integrator approach. Secondly, the nonlinear reduced-order compensator is designed for the subsystems of the planar...

Basic reproductive number for a general hybrid epidemic model

In this paper, a general hybrid epidemic model with multiple and non-periodic pulses in an environmental period is investigated. The definition and computation for the basic reproductive number R 0 $R_{0}$ are established. The published periodic research model (Yang, Xiao in Nonlinear Anal., Real World Appl. 52:224–234, 2012) can be considered as a special case of the new...

Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response

The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee effect and Holling type-III functional response. Instead of using classic first order differential equations to formulate the model, fractional order differential equations are...

Variable structure control for a singular biological economic model with time delay and stage structure

A singular biological economic model which considers a prey-predator system with time delay and stage structure is proposed in this paper. The local stability at the equilibrium point and the dynamic behavior of the model are studied. Local stability analysis of the model without time delay reveals that there is a phenomenon of singularity-induced bifurcation due to the economic...

Solvability for a class of evolution equations of fractional order with nonlocal conditions on the half-line

In this paper, we get a new form equivalent integral equation for a class of evolution equations of fractional order with nonlocal conditions on the half-line. With the aid of it, the uniqueness of the mild solution is obtained by the Banach contraction theorem. Also, we present the existence and uniqueness theorem of positive mild solutions by the monotone iterative method...

Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a maximum principle and a verification theorem for the Nash equilibrium point by virtue of the duality and convex variation approach. We study a linear-quadratic system under partial information...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

General solution to a higher-order linear difference equation and existence of bounded solutions

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

General solution to a higher-order linear difference equation and existence of bounded solutions

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Feedback control effect on the Lotka-Volterra prey-predator system with discrete delays

In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback...