Biological populations often exhibit complex and efficient behaviors, where temporal and spatial couplings at the macro-scale population level emerge from interactions at the micro-scale individual level, without any centralized control. This paper specifically investigates the emergence of behavioral synchronization and the division of labor in a foraging swarm of robotic agents. A deterministic model is proposed and used by each agent to decide whether it goes foraging, based on local cues about its fellow ants' behavior. This individual model, based on the competition of two spiking neurons, results in a self-organized division of labor at the population level. Depending on the strength and occurrences of interactions among individuals, the population behavior displays either an asynchronous, or a synchronous aperiodic, or a synchronous periodic division of labor. Further, the benefits of synchronized individual behaviors in terms of overall foraging efficiency are highlighted in a 2D spatial simulation.