Stability Analysis of the Ant System Dynamics with Non-uniform Pheromone Deposition Rules

This paper extends the classical Ant Systems by considering non-uniform deposition by the ants while constructing pheromone trails. A deterministic solution to the ant system dynamics for both uniform and non-uniform pheromone deposition rules has been obtained to determine the parameters of the dynamics that ensure stability in pheromone trails. The results of the stability analysis have been confirmed by extensive computer simulations. It is further noted that the Ant System (AS) employing exponential pheromone deposition rule yields better results in comparison to the one employing parabolic deposition rule.