Asymptotic Analysis and Identifiability of Nonlinear Differential Equations in Telecom Network Reliability in Rwanda: A Theoretical Framework

Theoretical analysis of nonlinear differential equations is a fundamental aspect of mathematical modelling in various fields including telecommunications network reliability. Theoretical derivations are employed to derive equations representing nonlinear differential models. Identifiability checks are conducted using statistical methods based on assumptions about the system parameters. The theoretical framework provides insights into the stability and predictability of telecom networks in Rwanda, offering a solid foundation for further empirical studies. Future research should validate these theoretical findings through practical application and identify potential areas for improvement in network design and operation. The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.