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  1. Content type: Research

    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 sys...

    Authors: Xiaozhou Feng, Yi Song, Jianxin Liu and Guohui Wang

    Citation: Advances in Difference Equations 2018 2018:314

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  2. Content type: Research

    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

    Authors: Shujing Gao, Yunbo Tu and Jialin Wang

    Citation: Advances in Difference Equations 2018 2018:310

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  3. Content type: Research

    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 feedba...

    Authors: Wei Zheng, Hongbin Wang, Hongrui Wang and Zhiming Zhang

    Citation: Advances in Difference Equations 2018 2018:312

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  4. Content type: Research

    This paper presents new results related to the coexistence of function-based hybrid synchronization types between non-identical incommensurate fractional-order systems characterized by different dimensions and or...

    Authors: Adel Ouannas, Giuseppe Grassi, Xiong Wang, Toufik Ziar and Viet-Thanh Pham

    Citation: Advances in Difference Equations 2018 2018:309

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  5. Content type: Research

    This paper studies a system of fractional differential equations with Riemann–Stieltjes integral conditions. The existence and uniqueness of nontrivial solutions to the above system are established under some ...

    Authors: Bingmei Liu, Junling Li, Lishan Liu and Yongqing Wang

    Citation: Advances in Difference Equations 2018 2018:306

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  6. Content type: Research

    In this paper, we define the q-analogue of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We study some approximation properties of these new operators, and we show that th...

    Authors: Serap Herdem and Ibrahim Büyükyazıcı

    Citation: Advances in Difference Equations 2018 2018:304

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  7. Content type: Research

    In this paper, we introduce two approaches to the generalized synchronized synchronization and the inverse generalized synchronization of fractional discrete-time chaotic systems with non-identical dimensions....

    Authors: Amina-Aicha Khennaoui, Adel Ouannas, Samir Bendoukha, Giuseppe Grassi, Xiong Wang and Viet-Thanh Pham

    Citation: Advances in Difference Equations 2018 2018:303

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  8. Content type: Research

    A two species stage-structured commensalism model is proposed and studied in this paper. Local and global stability property of the boundary equilibrium and the positive equilibrium are investigated, respectiv...

    Authors: Chaoquan Lei

    Citation: Advances in Difference Equations 2018 2018:301

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  9. Content type: Research

    Rossby waves, belonging to the most important waves in the atmosphere and ocean, can affect the energy transfer of the atmosphere and ocean and have significant theoretical meaning and research value. In previ...

    Authors: Mengshuang Tao, Ning Zhang, Dezhi Gao and Hongwei Yang

    Citation: Advances in Difference Equations 2018 2018:300

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  10. Content type: Research

    In this paper, based on gauge transformation of Lax pairs, we construct an N-fold Darboux transformation for the discrete Ragnisco–Tu equation which is a typical member in the Ragnisco–Tu hierarchy. By using the

    Authors: Ning Zhang, Tiecheng Xia and QiuYan Jin

    Citation: Advances in Difference Equations 2018 2018:302

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  11. Content type: Research

    Two new general classes of polynomial sequences called respectively odd and even Lidstone-type polynomials are considered. These classes include classic Lidstone polynomials of first and second kind. Some char...

    Authors: F. A. Costabile, M. I. Gualtieri, A. Napoli and M. Altomare

    Citation: Advances in Difference Equations 2018 2018:299

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  12. Content type: Research

    The computation of the viability kernel provides the guarantee for the security evolution of the systems. In this paper, we focus on the computation of the viability kernel for discrete-time and continuous-tim...

    Authors: Jianfeng Lv and Yan Gao

    Citation: Advances in Difference Equations 2018 2018:297

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  13. Content type: Research

    In this paper, stochastic effect on the spread of the infectious disease with saturated incidence rate and the special transfer from infectious is discussed. The threshold dynamics is explored for the case of ...

    Authors: Yi Song, Anqi Miao, Tongqian Zhang, Xinzeng Wang and Jianxin Liu

    Citation: Advances in Difference Equations 2018 2018:293

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  14. Content type: Research

    In this paper we present some global dynamic scenarios for general competitive maps in the plane. We apply these results to the class of second-order autonomous difference equations whose transition functions ...

    Authors: Elliott Bertrand and M. R. S. Kulenović

    Citation: Advances in Difference Equations 2018 2018:291

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  15. Content type: Research

    We study the results of existence and continuous dependence on neutral impulsive stochastic differential equations with Poisson jumps. We have also created some conditions confirming exponential stability.

    Authors: Anguraj Annamalai, Banupriya Kandasamy, Dumitru Baleanu and Vinodkumar Arumugam

    Citation: Advances in Difference Equations 2018 2018:290

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  16. Content type: Research

    Discrete N-fold Darboux transformation (DT) is used to derive new bright and dark multi-soliton solutions of two higher-order Toda lattice equations. Propagation and elastic interaction structures of such soliton...

    Authors: Nan Liu, Xiao-Yong Wen and Ling Xu

    Citation: Advances in Difference Equations 2018 2018:289

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  17. Content type: Research

    In this paper, we consider a Holling type II predator–prey model incorporating time delay and Allee effect in prey. We discuss the influence of Allee effect on the logistic equation. By analyzing the character...

    Authors: Zaowang Xiao, Xiangdong Xie and Yalong Xue

    Citation: Advances in Difference Equations 2018 2018:288

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  18. Content type: Research

    In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration t...

    Authors: Huiping Fang, Ling Hu and Yongfeng Wu

    Citation: Advances in Difference Equations 2018 2018:285

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  19. Content type: Research

    In this paper, an alternating segment Crank–Nicolson (ASC-N) parallel difference scheme is proposed for the time fractional sub-diffusion equation, which consists of the classical Crank–Nicolson scheme, four k...

    Authors: Lifei Wu, Xiaozhong Yang and Yanhua Cao

    Citation: Advances in Difference Equations 2018 2018:287

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  20. Content type: Research

    To quickly solve the fractional Black–Scholes (B–S) equation in the option pricing problems, in this paper, we construct pure alternative segment explicit–implicit (PASE-I) and pure alternative segment implici...

    Authors: Yue Li, Xiaozhong Yang and Shuzhen Sun

    Citation: Advances in Difference Equations 2018 2018:280

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  21. Content type: Research

    In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we are going t...

    Authors: Taekyun Kim, Dae San Kim, Dmitry V. Dolgy and Jin-Woo Park

    Citation: Advances in Difference Equations 2018 2018:277

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  22. Content type: Research

    In this paper, we investigate a delayed differential algebraic prey–predator system, where commercial harvesting on predator and additive Allee effect on prey are considered. A discrete time delay is utilized ...

    Authors: Chao Liu, Luping Wang, Na Lu and Longfei Yu

    Citation: Advances in Difference Equations 2018 2018:278

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  23. Content type: Research

    This paper proposes and analyzes an efficient compact finite difference scheme for reaction–diffusion equation in high spatial dimensions. The scheme is based on a compact finite difference method (cFDM) for t...

    Authors: Rongpei Zhang, Zheng Wang, Jia Liu and Luoman Liu

    Citation: Advances in Difference Equations 2018 2018:274

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    The Correction to this article has been published in Advances in Difference Equations 2018 2018:398

  24. Content type: Research

    The purpose of this paper is to present a methodological procedure to estimate the parameters of the exponential Ornstein–Uhlenbeck process, also known as the Schwartz (J. Finance 52(3):923–973, 1997) one-factor ...

    Authors: Carlos Armando Mejía Vega

    Citation: Advances in Difference Equations 2018 2018:269

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  25. Content type: Research

    The analytical and solitary traveling solutions of the nonlinear complex fractional generalized Zakharov equations are investigated. The nonlinear complex fractional generalized Zakharov equations describe the...

    Authors: Dianchen Lu, Aly R. Seadawy and Mostafa M. A. Khater

    Citation: Advances in Difference Equations 2018 2018:266

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Editors-in-Chief

agarwal_edit Ravi Agarwal, Texas A&M University, Kingsville, United States of America | 

Ravi's SpringerNature Publications

​​​​​​​mbnk_edit Martin Bohner, Missouri University of Science and Technology, United States of America | 

Martin's SpringerNature Publications

Elena_Braverman_image_edit Elena Braverman, University of Calgary Canada | 

Elena's SpringerNature Publications

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