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 of this title 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.

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