Advances in Difference Equations

http://www.advancesindifferenceequations.com/

List of Papers (Total 3,024)

Finite-time reliable filtering for T-S fuzzy stochastic jumping neural networks under unreliable communication links

This study is concerned with the problem of finite-time state estimation for T-S fuzzy stochastic jumping neural networks, where the communication links between the stochastic jumping neural networks and its estimator are imperfect. By introducing the fuzzy technique, both the nonlinearities and the stochastic disturbances are represented by T-S model. Stochastic variables...

Research on the Poincaré center-focus problem of some cubic differential systems by using a new method

In this article, we discuss the Poincaré center-focus problem of some cubic differential systems by using a new method (Mironenko’s method) and obtain some new sufficient conditions for a critical point to be a center. By using this method we not only solve a center-focus problem, but also at the same time, we open a class of differential systems, which do not have to be...

Global attractivity of an integro-differential model of competition

An integro-differential model of competition is studied in this paper. We show that the system always admits a unique globally attractive positive equilibrium. Our result complements and supplements the main result in the literature. MSC: competition model, integro-differential equation, delay, global attractivity.

A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative

We present a new method to investigate some fractional integro-differential equations involving the Caputo-Fabrizio derivation and we prove the existence of approximate solutions for these problems. We provide three examples to illustrate our main results. By checking those, one gets the possibility of using some discontinuous mappings as coefficients in the fractional integro...

Solvability of triple-point integral boundary value problems for a class of impulsive fractional differential equations

This paper is concerned with a class of triple-point integral boundary value problems for impulsive fractional differential equations involving the Riemann-Liouville fractional derivative of order α ( 2 < α ≤ 3 ). Some sufficient criteria for the existence of solutions are obtained by applying the contraction mapping principle and the fixed point theorem. As an application, one...

Periodicity in a neutral predator-prey system with monotone functional responses

By utilizing the coincidence degree theory and the related continuation theorem, as well as some prior estimates, we investigate the existence of positive periodic solutions of a neutral predator-prey system with monotone functional responses. New sufficient criteria are established for the existence of periodic solutions. Some well-known results in the literature are generalized...

Existence and multiplicity of solutions for a second-order impulsive differential equation via variational methods

In this paper, we study the existence and multiplicity of solutions for an impulsive differential equation via some critical point theory and the variational method. We extend and improve some recent results and reduce conditions.

Homoclinic orbits for a class of second order dynamic equations on time scales via variational methods

In this paper, we study the existence of nontrivial homoclinic orbits of a dynamic equation on time scales T of the form { ( p ( t ) u Δ ( t ) ) Δ + q σ ( t ) u σ ( t ) = f ( σ ( t ) , u σ ( t ) ) , △ -a.e.  t ∈ T , u ( ± ∞ ) = u Δ ( ± ∞ ) = 0 . We construct a variational framework of the above-mentioned problem, and some new results on the existence of a homoclinic orbit or an...

Existence of nonoscillatory solutions for system of higher-order neutral differential equations with distributed coefficients and delays

In this paper we consider the existence of nonoscillatory solutions for a system of higher-order neutral differential equations with distributed coefficients and delays. We use the B a n a c h contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.

Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model

This paper considers two kinds of novel decoupled algorithms for the non-stationary Stokes-Darcy model. In this way, the considered problem is decoupled into one time-dependent Stokes equations and one linear parabolic equation. For the two algorithms, we establish the stability and the optimal error estimates. Furthermore, the existing result in Mu and Zhu (Math. Comput. 79:707...

On the quartic Gauss sums and their recurrence property

The main purpose of this paper is, using the method of trigonometric sums and the properties of Gauss sums, to study the computational problem of one kind of congruence equation modulo an odd prime and give some interesting fourth-order linear recurrence formulas. MSC: 11L05.

Finite-time control for uncertain systems with nonlinear perturbations

This study investigates the problem of finite-time control for uncertain systems with nonlinear perturbations. The aim is to design the state-feedback and output-feedback controller which ensure finite-time boundedness and with a desired H ∞ performance index υ. Specifically, first, we divide the time-varying delay into non-uniformly subintervals and decompose the corresponding...

The joint effects of diffusion and delay on the stability of a ratio-dependent predator-prey model

This paper is concerned with a diffusive and delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary conditions. Preliminary analyses on the well-posedness of solutions and the dissipativeness of the system are presented with assistance of inequality technique. Then the Hopf bifurcation induced by spatial...

Growth of meromorphic solutions of certain types of q-difference differential equations

In this paper, relying on Nevanlinna theory of the value distribution of meromorphic functions, we mainly study meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their meromorphic solutions, and give a number of examples to show what our results are the best possible in certain senses. Improvements and...

Absolute stability of time-varying delay Lurie indirect control systems with unbounded coefficients

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative...

On solutions of fractional Riccati differential equations

We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of...

Existence of positive solutions for integral boundary value problems of fractional differential equations with p-Laplacian

This paper is concerned with the existence of positive solutions for integral boundary value problems of Caputo fractional differential equations with p-Laplacian operator. By means of the properties of the Green’s function, Avery-Peterson fixed point theorems, we establish conditions ensuring the existence of positive solutions for the problem. As an application, an example is...

A new method to study ILC problem for time-delay linear systems

In this paper, we apply a new method, a delayed matrix exponential, to study P-type and D-type learning laws for time-delay controlled systems to track the varying reference accurately by using a few iterations in a finite time interval. We present open-loop P- and D-type asymptotic convergence results in the sense of λ-norm by virtue of spectral radius of matrix. Finally, four...

Passivity analysis and state estimation for a class of memristor-based neural networks with multiple proportional delays

This paper is concerned with the problem of a passivity analysis for a class of memristor-based neural networks with multiple proportional delays and the state estimator is designed for the memristive system through the available output measurements. By constructing a proper Lyapunov-Krasovskii functional, new criteria are obtained for the passivity and state estimation of the...

Estimation of parameters in a structured SIR model

In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model...

Qualitative analysis for a delayed epidemic model with latent and breaking-out over the Internet

We generalize a delayed computer virus model, known as the SLBQRS model in a computer network, by introducing the time delay due to the period that the antivirus software uses to clean viruses in the breaking out computers and the quarantined computers. By choosing the delay as the parameter, we prove the existence of a Hopf bifurcation as the delay crosses a critical value...

Oscillation of Runge-Kutta methods for advanced impulsive differential equations with piecewise constant arguments

The purpose of this paper is to study oscillation of Runge-Kutta methods for linear advanced impulsive differential equations with piecewise constant arguments. We obtain conditions of oscillation and nonoscillation for Runge-Kutta methods. Moreover, we prove that the oscillation of the exact solution is preserved by the θ-methods. It turns out that the zeros of the piecewise...

The extinction and persistence of a stochastic SIR model

The objective of this paper is to explore the long time behavior of a stochastic SIR model. We establish a threshold condition called the basic reproduction number under stochastic perturbation for persistence or extinction of the disease. Especially, some numerical simulations are applied to support our theoretical results. MSC: 49K15, 60H10, 93E15.

The modified degenerate q-Bernoulli polynomials arising from p-adic invariant integral on Z p

Dolgy et al. introduced the modified degenerate Bernoulli polynomials, which are different from Carlitz’s degenerate Bernoulli polynomials (see Dolgy et al. in Adv. Stud. Contemp. Math. (Kyungshang) 26(1):1-9, 2016 ). In this paper, we study some explicit identities and properties for the modified degenerate q-Bernoulli polynomials arising from the p-adic invariant integral on Z...

Hopf bifurcations in an extended Lorenz system

In this work, we study Hopf bifurcations in the extended Lorenz system, x ˙ = y , y ˙ = m x − n y − m x z − p x 3 , z ˙ = − a z + b x 2 , with five parameters m , n , p , a , b ∈ R . For some values of the parameters, this system can be transformed to the classical Lorenz system. In this paper, we give conditions for occurrence of Hopf bifurcation at the equilibrium points. We...