In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported.

在本文中，正在考虑使用非线性修改的Gardner（mG）方程，该方程表示离子声波和量子电子-正电子磁等离子体的超非线性扩散。在李群分析的帮助下研究了所考虑的模型。根据Lie组的不变性标准计算Lie点对称性，并报告每个生成器的对称性组。此外，通过伴随技术开发了一维最优子代数系统，然后我们计算了与最优系统中存在的每个矢量场相对应的相似度约简，借助相似度约简方法，我们必须将PDE转换为ODE。利用幂级数技术构造了获得的常微分方程的一些精确显式解。借助伽利略变换，将模型变换为平面动力学系统，并记录分叉行为。绘制了与所考虑问题的参数有关的所有可行类型的相图。同时，通过利用灵敏度分析来观察灵敏度。另外，通过应用外部周期性功率来研究物理参数的影响。加上额外的扰动项，据报道出现了准周期和准周期混沌行为。物理参数的影响通过外在周期性功率的应用来研究。加上额外的扰动项，据报道出现了准周期和准周期混沌行为。物理参数的影响通过外在周期性功率的应用来研究。加上额外的扰动项，据报道出现了准周期和准周期混沌行为。