Bifurcation and chaotic patterns of the solitary waves in nonlinear electrical transmission line lattice

The theory of bifurcation is applied to generate chirp of the soliton within a nonlinear electrical lattice featuring next-neighbor couplings. By employing the reductive perturbation method, we derive the Chen–Lee–Liu equation, thereby obtaining the nonlinear system in a planar form. Bifurcation analysis of the phase portraits is conducted to demonstrate the emergence of homoclinic and heteroclinic orbits from the equilibrium points. These orbits serve as evidence that the nonlinear electrical network with neighbor couplings supports a diverse range of wave phenomena, including bright, dark, kink, and double-kink waves, as well as periodic waves. Furthermore, an external force is introduced to investigate the chaotic, quasi-periodic and time-dependent behaviors within the nonlinear system. It becomes evident that both the phase portraits and the time-dependent waveforms are highly responsive to variations in the amplitude of the external force. Finally, it is noteworthy that the Chen–Lee–Liu equation derived in the electrical network with neighbor couplings sheds light on dynamic behaviors reminiscent of those observed in models such as the helicoidal Peyrard–Bishop–Dauxois model of deoxyribonucleic acid and anharmonic lattices (Djine et al., 2023; Tchakoutio Nguetcho et al., 2017).