Cooperating swarms: A paradigm for collective intelligence and its application in finance.

The control of nonlinear chaotic system and the estimation of parameters is a vital issue in nonlinear science. Studies on parameter estimation for chaotic systems have been investigated recently. A variant of Particle Swarm Optimization (PSO) known as Chaotic Multi Swarm Particle Swarm Optimization (CMS-PSO) is proposed which is inspired from the metaphor of ecological co-habitation of species. The generic PSO is modified with the chaotic sequences for multi-dimension parameter estimation and optimization by forming multiple cooperating swarms. Results demonstrate the effectiveness of the scheme in successfully estimating the unknown parameters of a new hyperchaotic finance system. Numerical results and comparison demonstrate that for the given parameters of the nonlinear system, CMS-PSO can identify the optimized parameters effectively to reach the pareto optimal solution and convergence speed.