Analyzing Bifurcation, Stability, and Wave Solutions in Nonlinear Telecommunications Models Using Transmission Lines, Hamiltonian and Jacobian Techniques

Abstract This study delves into the analysis of bifurcation in a nonlinear model pertinent to the telecommunications industry. Employing Hamiltonian and Jacobian techniques, we explore numerical solutions and analytic nonlinear wave solutions in alignment with energy orbits depicted in phase portraits. The stability of critical points is addressed through graphical representations and numerical analyses. Moreover, the investigation extends to traveling wave solutions. The paper concludes by presenting graphical insights into how parameters influence wave solutions, emphasizing the efficacy of the planar dynamical approach.