This paper explores novel concepts within perturbed models, focusing on their local stability analysis of fixed points. The investigation involves numerical simulations employing bifurcation diagrams and phase diagrams to substantiate findings and delineate intricate dynamics. By leveraging these computational tools, the research aims to validate its results comprehensively.

Moreover, the theoretical implications of these new concepts are thoroughly scrutinized and compared with existing frameworks. This comparative analysis sheds light on the advancements introduced by the proposed models, highlighting their potential contributions to the field. Through rigorous examination and validation via simulations and theoretical scrutiny, the study not only confirms the stability properties of fixed points under perturbations but also elucidates the broader implications of these findings.

Furthermore, the utilization of bifurcation and phase diagrams serves to illustrate the complex behaviors and transitions observed within the models, offering a visual representation that enhances the understanding of the dynamics involved. Overall, this paper contributes to advancing the understanding of perturbed models by integrating theoretical insights with numerical validation, thus paving the way for future research in this area.