A computer-implemented method for multi-mode operation of a combustion system, a combustion system, and a heat engine are provided. The method includes initializing combustion of a fuel/oxidizer mixture, determining whether conditions at the combustion system meet or exceed a first threshold operating parameter, transitioning to detonation combustion of the fuel/oxidizer mixture if conditions at the combustion system meet or exceed the first threshold operating parameter, and maintaining or increasing fuel flow through a deflagrative fuel circuit if conditions at the combustion system do not meet or exceed the first threshold operating parameter.