Bifurcation of low-frequency ion-acoustic nonlinear structures and chaos with fractional effect in Non-Maxwellian magnetoplasmas

The dynamics of ion-acoustic waves (IAWs) in nonextensive magnetoplasmas with the two-temperature electrons are studied. The plasma model equations are transformed into the modified Korteweg–de Vries equation employing the reductive perturbation method. The Grunwald–Letnikov definition and the Newton–Leipnik algorithm are addressed to study the forced dynamical system. Through the fourth-order Runge–Kutta scheme, the fractional forced system is solved numerically. It is seen that the quasi-period route to chaos is impacted by the fractional parameter α in a forced system. It is also found that both regular and irregular oscillations appear due to the variations in the fractional-order term. Phase portrait plots, time series, and bifurcation diagrams corroborate these results. The relevance of this investigation can help to understand the problem of anomalous transport due to the drift wave turbulence state of the plasma.