Qualitative Analysis of Discrete Dynamical Systems Involving k-Mersenne Numbers

This paper studies the dynamics of a nonlinear difference system related to the k-Mersenne sequence a generalization of classical Mersenne numbers. By transforming the nonlinear system into a linear form, explicit solutions are obtained in terms of k-Mersenne numbers. The analysis establishes the global asymptotic stability of the system’s positive equilibrium and characterizes the convergence rate using the Jacobian’s spectral radius. Numerical examples confirm the theoretical findings and illustrate the system’s stability and behavior. MSC Classification: 39A10 , 40A05.