The 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.

中文翻译：

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非热电子尘埃等离子体中尘埃离子声波传播的分岔类型及动态控制

研究了由暖绝热离子、非热电子和静止冷尘粒组成的尘埃等离子体中非线性尘埃离子声行波的分岔类型和相图。推导出等离子体波演化的动力学系统，然后在平衡点-非热参数平面上确定分岔响应。结果表明，对于高能电子的临界值，行波的运动动力学经历了跨临界以及鞍节点分岔。我们指出，孤立波和非线性周期波之间的突然出现和过渡发生在跨临界分岔的临界点。对于鞍节点分岔，我们表明孤立和超非线性周期波都消失了，只有大振幅的周期波才能在等离子体中传播。此外，针对不同的等离子体参数值，研究了孤立波、非线性波和超非线性波的共存情况。这里获得的结果可能适用于不同的空间和天体物理等离子体系统，特别是在土星的 E 环中。