Bifurcation types and dynamic control of dust ion‐acoustic waves propagation in dusty plasmas with non‐thermal electrons

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AbstractThe bifurcation types and phase portraits of non‐linear dust ion‐acoustic travelling waves are studied in a dusty plasma comprising warm adiabatic ions, non‐thermal electrons and stationary cold dust species. A dynamical system is derived for the plasma waves evolution, and then the bifurcation response is determined on the equilibrium points‐non‐thermal parameter plane. It is shown that the motion dynamics of travelling waves undergoes a transcritical as well as saddle‐node bifurcations for the critical values of energetic electrons. We indicate that a sudden emergence and transition between solitary waves and non‐linear periodic waves occur at the critical point of transcritical bifurcation. For the saddle‐node bifurcation, we show that both solitary and super‐nonlinear periodic waves disappear, and only a large amplitude periodic wave can propagate in plasma. Further, the coexistence of solitary waves, non‐linear and super‐nonlinear waves are investigated for different values of plasma parameters. The results obtained here could be applicable to different space and astrophysical plasma systems, particularly in Saturn's E‐ring.