Dynamical behavior of Lakshamanan-Porsezian-Daniel model with spatiotemporal dispersion effects

Abstract

The dynamical behavior of the Lakshamanan-Porsezian-Daniel (LPD) model with applications in nonlinear optics is uncovered in this paper. The incorporation of spatio-temporal dispersion into the model, addressing the internet bottleneck issue, is emphasized. A planar dynamical system (DS) is accounted for by applying the Galilean transformation to the considered model. All types of phase portraits are plotted based on specific values of parameters. For the generation of quasi-periodic and chaotic patterns, Acos⁡(Ωτ) with strength and frequency components is added. The resulting quasi-periodic and chaotic orbits are also plotted. Various bifurcation and chaos detecting tools, such as time series analysis, Poincare maps, Lyapunov exponent, bifurcation diagrams, and sensitivity, are employed to examine the behavior of the obtained dynamical system under proposed initial conditions. The Hamiltonian function is calculated and plotted for the unperturbed dynamical system. Multi-stability phenomena demonstrate the coexistence of multi-stable orbits in their dynamic features. The dynamics of pulse propagation are found to be significantly impacted by the spatio-temporal dispersion.

Keywords

• Lakshamanan-Porsezian-Daniel model
• Parabolic law
• Phase diagrams
• Chaos
• Hamiltonian
• Poincare maps