This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures.

Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems.

The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in differential equations and applications.

Table of Contents

• H. Brunner -- The discretization of Volterra functional integral equations with proportional delays
• J. M. Cushing -- The LPA model
• X. Z. Qian and Z. C. Wang -- A survey on oscillation of linear delay difference equations
• Y. Yi -- On almost automorphic oscillations

• R. M. Abu-Saris and K. I. Al-Dosary -- Complex exponential Vandermonde determinant with application to discrete boundary value problem
• Y. Cao -- A convergence theorem related to iterative mean clustering
• A. Chen and L. Huang -- Global attractivity in a model of bobwhite quail with delay
• S. S. Cheng, C.-W. Chen, and T. Y. Wu -- Linear time discrete periodic diffusion networks
• B. Dai, X. Qian, and L. Huang -- Convergence of solutions for a discrete-time system
• T. Furumochi, S. Murakami, and Y. Nagabuchi -- Stabilities in Volterra difference equations on a Banach space
• S. Guo and L. Huang -- Periodic oscillation for a class of delay difference systems
• Z. Guo and J. Yu -- Applications of critical point theory to difference equations
• D. Levi -- Lie symmetries for lattice equations
• X. Li and Z. Wang -- Global attractivity for a logistic equation with piecewise constant arguments
• X. Lin -- Bounded oscillation for a class of second order neutral delay difference equations
• K. Liu and H. Zhang -- Asymptotic behavior in nonlinear discrete-time neural networks with delayed feedback
• Y. Liu, L. Huang, and Z. Yuan -- Asymptotic behavior and periodicity of solutions for a difference equation with piecewise constant nonlinearity
• Y. Liu, Z. Zhou, and W. Ge -- Positive solutions of a non-autonomous delay model of single population
• H. Matsunaga -- Stability regions for a class of delay difference systems
• M. Migda -- Oscillation and nonoscillation results for higher-order nonlinear difference equations
• C. Pötzsche -- Stability of center fiber bundles for nonautonomous difference equations
• R. J. Sacker and H. F. von Bremen -- Bifurcation of maps and cycling in genetic systems
• E. Schmeidel -- Nonoscillation and oscillation theorems for a fourth order nonlinear difference equation
• H. Sedaghat -- On the equation \(x_{n+1}=cx_{n}+f(x_{n}-x_{n-1})\)
• C. Tian, J. Zhang, and Z. Ji -- Stability criteria for a kind of delay functional equation
• L. Wang and X. Zou -- Exponential stability of delay difference equations with applications to neural networks
• X. Wang and L. Liao -- Asymptotic behavior of solutions of linear difference-differential equations with oscillating coefficients
• W. Wendi -- Analysis of a discrete predator-prey model
• H.-W. Wu and Y.-T. Xu -- Oscillation for nonautonomous neutral difference equations with variable coefficients
• Z. Yinggao -- Oscillation of higher-order nonlinear delay difference equations
• Z. Yuan, L. Huang, and Z. Zhou -- Coexistence of multiple attractive periodic solutions in a discrete-time neural network
• R. Y. Zhang, Z. C. Wang, and J. S. Yu -- Necessary and sufficient conditions for the existence of positive solutions of nonlinear difference equations
• Z. Zhou and Q. Zhang -- Periodic solutions of a class of difference systems
• H. Zhu and L. Huang -- Dynamic analysis of a discrete-time network of two neurons with delayed feedback

• S. Elaydi -- Open problems and conjectures
• H. Brunner -- Discretization of Volterra integral equations with weakly singular kernels
• S. Elaydi -- Nonautonomous difference equations: Open problems and conjectures
• E. A. Grove and G. Ladas -- On period-two solutions of \(x_{n+1} =\frac{\alpha + \beta x_{n}+\gamma x_{n-1}}{A + Bx_{n}+ C x_{n-1}}\)
• R. J. Sacker and H. F. von Bremen -- Open problems on cycling in genetic systems
• J. Wu -- On periodic solutions of systems of two difference equations