First-order expansions of coupled Leonardo sequences

Resumo

In this paper, we investigate the sensitivity of coupled Leonardo sequences under perturbations of the recurrence coefficients and the coupling term. By introducing a perturbation parameter, we derive an explicit first-order asymptotic expansion and establish a linear sensitivity equation governing the leading correction term. Under suitable spectral assumptions, we obtain uniform error estimates and show that the perturbed sequence admits a first-order approximation whose accuracy is controlled by the perturbation magnitude. These results provide a quantitative description of the stability and local behavior of coupled Leonardo sequences and contribute to the perturbation theory of linear recursive systems.