Spike-Like Traveling Waves at the Critical Point of Bifurcation in a Nonextensive Dusty Plasma With Dust Polarity

This article presents a detailed study on the basic features of bifurcation of dust ion acoustic (DIA) traveling waves in a dusty plasma comprising warm adiabatic ions, nonextensive electrons, and arbitrarily charged dust particles. A reduced dynamical system is obtained for plasma waves’ evolution, and the global dynamics of local bifurcation of waves’ motion are determined on the equilibrium points’ dust concentrations’ plane with respect to all possible plasma parametric combinations. The stability and phase portrait analysis indicate a sudden emergence of nonlinear periodic and solitary waves for critical values of negative (positive) dust concentration. At these critical values, waves’ dynamics exhibit a transcritical bifurcation with half-stable fixed points which support new spike-like traveling waves. The analytical and numerical solutions reveal that the decay rate of this localized structure is much slower than ordinary solitary waves that decay exponentially fast. Furthermore, the existence domain of bifurcation parameters and transitions between modes are found for different values of nonextensive electrons and arbitrarily charged dust concentrations. Our results could be applicable to different space and astrophysical plasma systems, particularly in earth atmosphere.