Solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in nonextensive dusty plasmas

Abstract

The solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in an unmagnetized dusty plasma with q-nonextensive electrons are studied using the bifurcation theory of planar dynamical systems through direct approach. Using Galilean transformation, model equations are transformed to a planar dynamical system. We obtain all possible phase portraits of the planar dynamical system and corresponding solitary and periodic wave solutions depending on parameters q and μ. Considering an external periodic perturbation, the quasiperiodic and chaotic behaviors of dust ion acoustic waves are presented. The effect of q, the nonextensive parameter is found to have significant effect on quasiperiodic and chaotic motions of dust ion acoustic waves. To show these we study the behavior of dust ion acoustic waves for several values of q, keeping the other plasma parameters like μ and v fixed. It is seen that the unperturbed dynamical system has the solitary and periodic wave solutions, but the perturbed dynamical system has quasiperiodic and chaotic motions for same values of parameters q,μ and v.