Bifurcation analysis of dust acoustic (DA) periodic waves in three components, unmagnetized dusty plasma system is investigated using the generalized (r, q) distribution function for ions and electrons. Depending on the different parameters of the system considered, all possible phase portraits, including periodic, homoclinic, superperiodic, and superhomoclinic trajectories, are presented. The existence of rarefactive and compressive solitary waves is proved. Also, the plasma system under consideration supports both nonlinear and supernonlinear DA periodic waves. It has been found that the double spectral indices r and q play a decisive effect on the bifurcation of the waves.

中文翻译：

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尘埃等离子体中非线性和超非线性尘埃声波的分叉分析，使用离子和电子的广义（r，q）分布函数

利用离子和电子的广义（r，q）分布函数，研究了非磁化尘埃等离子体系统三个分量中的尘埃声波（DA）周期波的分叉分析。根据所考虑系统的不同参数，显示了所有可能的相图，包括周期性，同斜，超周期和超斜向轨迹。证明了稀疏和压缩孤波的存在。而且，所考虑的等离子体系统支持非线性和超非线性DA周期波。已经发现，双光谱指数r和q对波的分叉起决定性作用。