Deterministic Chaos, Bifurcations and Strange Attractors in Nonlinear Dynamics of Relativistic Backward-Wave Tube

Глушков, А. В.; Цудік, А. В.; Ternovsky, V. B.; Astaykin, Dmytro V.; Бондаренко, Андрій Володимирович; Danylenko, Dmytro V.; Buyadzhi, V. V.

doi:10.1007/978-3-030-77310-6_12

Cited by 1 publication

(1 citation statement)

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“…The dynamical behavior of nonlinear physical systems is currently a popular area for study in the nonlinear sciences. Several scientists are researching chaotic and bifurcation dynamics for nonlinear physical systems [32][33][34][35][36][37][38]. The bifurcations and chaotic trajectories of the ion-acoustic waves in a magnetized Auroral zone plasma were recovered by Prasad et al [39].…”

Section: Introductionmentioning

confidence: 99%

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Muhammad,

Abbas,

Hussain

et al. 2024

Phys. Scr.

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In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I \& II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters $d_1$ and $d_3$. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

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