<p>Current research on vehicular platoon control rarely considers the nonlinear tire force of vehicles, thus potentially failing to maintain stability under critical conditions, such as high-speed driving on low-adhesion roads. To solve it, this study investigates the nonlinear dynamic characteristics of the bidirectional following (BD) platoon, which offers promising practical prospects and improved performance by simply adding rear-detection sensors based on the predecessor following (PF) platoon. The critical conditions are investigated from the perspective of platoon-vehicle integrated dynamics, thereby providing a solid theoretical basis for the design of control strategies of BD platoons in practical applications. A platoon-vehicle coupled nonlinear dynamic system is established with the incorporation of nonlinear tire forces. The head-to-tail transfer function including the dynamics of all following vehicles is derived. The equilibrium stability and head-to-tail string stability of the platoon under critical conditions are addressed through the influence law in the parameter space of control gains with respect to the predecessor. The results demonstrate that the stability parameter space of the platoon under critical conditions is quite limited. Moreover, given that the string stability parameter space is a subset of the equilibrium stability parameter space, the controller design should primarily focus on the string stability parameter space under critical conditions, and the beneficial effect of the expanded string stability parameter space when transforming a PF platoon into a BD platoon obviously outweighs the detrimental effect of the reduced equilibrium stability parameter space.</p>