Advances in Difference Equations is a peer-reviewed open access journal published under the brand SpringerOpen. The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 12 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. Articles published in Advances in Difference Equations will include such situations. The aim of Advances in Difference Equations is to report new developments in the field of difference equations, and their applications in all fields. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
Advances in Difference Equations
Description
Identifiers
e-ISSN | 1687-1847 |
DOI | 10.1007/13662.1687-1847 |
Publisher
Springer International Publishing
Additional information
Data set: Springer
Articles
Advances in Difference Equations > 2019 > 2019 > 1 > 1-15
In this paper, by means of a proper orthogonal decomposition (POD) we mainly reduce the order of the classical Crank–Nicolson finite difference (CCNFD) model for the fractional-order parabolic-type sine-Gordon equations (FOPTSGEs). Toward this end, we will first review the CCNFD model for FOPTSGEs and the theoretical results (such as existence, stabilization, and convergence) of the CCNFD solutions...
Advances in Difference Equations > 2019 > 2019 > 1 > 1-14
In this paper, a predator–prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the homoclinic cycle is obtained by analyzing the control parameter q. The existence, uniqueness and asymptotic stability of the periodic orbit are discussed by using the geometric theory of the...
Advances in Difference Equations > 2019 > 2019 > 1 > 1-22
In this paper, we study the periodic solutions of high order differential delay equations with 2k−1 lags. The 4k-periodic solutions are obtained by using the variational method and the method of Kaplan–Yorke coupling system. These are new types of differential delay equations compared with all previous research. And it provides a precise counting method for the number of periodic solutions....