Speaker
Description
We investigate the local dynamics of a class of (p)-dimensional nonlinear rational difference equation systems with power-type nonlinearities, extending several previously studied low-dimensional models to a general higher-dimensional setting. The analysis focuses on the boundedness of solutions and the local asymptotic stability of equilibrium states. By establishing explicit sufficient conditions for stability, we identify the influence of the system parameters on the qualitative behavior of trajectories near equilibria. Beyond extending existing theoretical results, the proposed framework provides a unified approach for analyzing high-dimensional discrete nonlinear systems and reveals structural features governing their local dynamics. Although the present work does not deal directly with soliton solutions, the stability techniques and dynamical analysis developed here contribute to the broader understanding of nonlinear discrete models that arise in the study of nonlinear wave propagation, lattice dynamics, and related evolution phenomena, making the results relevant to the general themes of nonlinear dynamics addressed by the workshop.