Adaptive Cycle Engines (ACEs) emerge as a promising solution to fulfill the diverse mission requirements of next-generation aircraft, with advanced control strategies being pivotal for optimizing ACE performance. This study initially delineates the fundamental mechanisms of ACE, encompassing the mode selection valve, variable area duct injector, and other key components, culminating in the development of an accurate dynamic component-level nonlinear model for ACE. Given the complexity of ACE’s structure and the multitude of iterative variables, the paper introduces an intelligent hybrid solving algorithm aimed at enhancing the convergence rate of nonlinear model solutions. Initially employing the Newton-Raphson optimization algorithm for iterative solutions, the method transitions to the Honey Badger algorithm when convergence becomes challenging, resulting in a 61.7% improvement in solution convergence rate compared to the conventional Newton-Raphson approach. Further, the paper conducts a comparative analysis of ACE characteristics under dual and triple bypass modes, meticulously examining parameters such as compressor speed percentage, specific fuel consumption, CDFS surge margin, and compressor surge margin. The analysis reveals that the specific fuel consumption in the triple bypass mode is 10.3% lower than that in the dual bypass mode, and the established component-level nonlinear model proficiently simulates the dynamic characteristics of adaptive cycle engines.