Stability and bifurcation analysis of nonlinear ion-acoustic waves in superthermal electron-positron-ion plasmas

In this study, the stability and bifurcation analysis of nonlinear ion-acoustic waves is investigated in a non-Maxwellian plasma consisting of cold ions and Kappa-distributed electrons and positrons.  First, a characteristic equation for the evolution of ion-acoustic waves is obtained and then the stability of traveling wave solution on fixed points-energetic positron density plane is discussed numerically. It is found that the motion dynamics of homoclinic orbits and nonlinear periodic orbits undergo a transcritical bifurcation at the critical positron density , where two fixed points coalesce, and then switch their stabilities. The variations of the initial  and critical  positron concentrations versus a wide range of values of the spectral index of positrons  and electron-to-positron temperature ratio  are also studied. Furthermore, according to the phase portraits analysis, the coexistence of homoclinic orbits, nonlinear periodic, and super nonlinear periodic orbits is also investigated for different conditions. It is shown that the positron density and the temperature ratio of electron to positron play a crucial role in the propagation of nonlinear waves.