Bifurcation Analysis of Ion-Acoustic Waves in a Dusty Plasma

In this work, the stability and instability of low- frequency electrostatic waves (i.e., ion-acoustic waves) in a dusty plasma consisting of cold ions and non-thermal electrons with a combined Kappa-Cairns distribution are investigated. The basic equations to describe the plasma and the dynamic equation of the present system are determined. It is observed that the presence of the high -energy electrons has a significant effect on the ion-acoustic wave structures. The numerical results have shown that dust particles can also change the stability of the system. Moreover, according to phase space analysis, the presence of homoclinic, nonlinear periodic as well as super-periodic circuits have also been investigated for different conditions. Therefore, in this system, due to a small change in the value of plasma parameters, we will see different behavior for the ion-acoustic waves.