Abstract
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.