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Online task scheduling in heterogeneous multicore system-on-a-chip is a challenging problem due to precedence constraints and nonpreemptive task execution in the synergistic processor core. This study first proposes an online heterogeneous dual-core scheduling framework for dynamic workloads with real-time constraints. The general purpose processor core and the synergistic processor core are dedicated to separate schedulers with different scheduling policies, and precedence constraints among tasks are dealt with through interaction between the two schedulers. This framework is also configurable for low priority inversion and high system utilization. We then extend this framework to heterogeneous multicore systems with well-known dispatcher schemas. This paper presents a real case study to show the practicability of the proposed methodology, and presents a series of extensive simulations to obtain comparison studies using different workloads and scheduling algorithms.