Parameter estimation of a generalized Lotka–Volterra system using a modified PSO algorithm

Abstract

In this study, parameter estimation of a generalized Lotka–Volterra system for three competing species is formulated as a multidimensional optimization problem. A modified version of a particle swarm algorithm is applied to solve it. The proposed algorithm, PSO+, adds a new term to the standard PSO to diversify and improve search capability. First, a set of five benchmark functions was used to test the proposed algorithm, solving the global minimum localization problem. Once tested, the algorithm was used to estimate the parameters of a three-dimensional two-predator–one-prey system under conditions of chaotic behavior. Numerical simulations show the PSO+ increases accuracy by ∼10% over standard PSO in the parameter estimation problem. Also, PSO+ can reconstruct the attractor and Lyapunov exponents of the system with MSE < 0.0001. Results show that the PSO+ algorithm can be a useful and powerful computational technique for parameter estimation of dynamical/chaotic systems, with accurate performance and very low deviations.