Ant foraging behavior has inspired research in a number of areas including distributed problem solving such as optimization and task allocation and mobile robot navigation. In the area of swarm robotic systems, ant foraging behavior has been largely modeled via behavior based techniques and analyzed using cellular automata. Development of continuous time models for ant foraging can potentially provide insights into new mechanisms and behaviors used by ants that provide self-organizing capabilities to the ant colony. This paper presents a distributed control law in continuous time that combines gradient following for pheromone concentration as well as food scent with random motion seen in ants. The paper also provides a continuous time model for pheromone laying in a 2D environment and carries out a preliminary numerical stability analysis of the solutions. Extensive simulation studies confirm emergent behaviors seen in ant systems such as trail formation and convergence to single food site. In addition, the paper examines the effect of randomness on robustness of convergence to a single food site.