A frequency domain analysis on the deterministic modeling of the Ant System dynamics

This paper presents a deterministic model of Ant System and its subsequent frequency domain analysis. Classical Ant System is modeled as a first order and first degree differential equation form without violating the stochastic nature of the ant dynamics. Then, a transfer function model is developed and the system characterization is done in frequency domain. It is helpful to explore the system behavior that gives the supportive analysis on the stability of the Ant System. Also we analyze the necessary bounds of the trail persistence P which will control the ant dynamics to avoid over accumulation of pheromone and help to find good optimal solution. The outlook of this deterministic solution is to ensure stability and investigate the convergence criterion in pheromone trail which satisfactorily establishes the significance of the transfer function model of the ant system dynamics. Simulation results also represent supportive evidence of this analytical analysis.