An in-depth bifurcation analysis is carried out for the peristaltic transport of non-Newtonian fluid with heat and mass transfer through an axisymmetric channel. Based on the perturbation technique, analytical solutions for flow rate and stream function are presented. This function and its velocity fields build a nonlinear dynamic system in two spatial dimensions. We are then interested in identifying the global and local bifurcation of the invariant curves in which the recurrent fluid dynamics close to the stagnation points change qualitatively. For this purpose, a geometric description, analytical expressions and the development of a computational algorithm are provided to recognize the multiplicity of admissible/virtual stagnation points. In a variety of physical parameters, the analysis highlights the presence of several types of nonlinear phenomena, such as infinite/finite heteroclinic and homoclinic orbits, saddle-node and border-collision bifurcations. These results guide the streamline patterns for capturing novel complex behaviors such as multiple trapping phenomena and critical transition to distinguish between different flow regions.

对非牛顿流体通过轴对称通道进行传热和传质的蠕动传输进行了深入的分叉分析。基于扰动技术，提出了流速和流函数的解析解。该函数及其速度场在两个空间维度上构建了非线性动力学系统。然后，我们对确定不变曲线的全局和局部分歧感兴趣，在不变曲线中靠近停滞点的循环流体动力学发生质的变化。为此，提供了几何描述，解析表达式和计算算法的开发，以识别可允​​许的/虚拟的停滞点的多样性。在各种物理参数中，分析强调了几种类型的非线性现象的存在，例如无限/有限的异斜率和同斜率轨道，鞍节点和边界碰撞分叉。这些结果指导了流线型模式，以捕获新颖的复杂行为，例如多种捕获现象和临界转变，以区分不同的流动区域。