A SwarmIntelligence Approach toParameters Identification ofChaotic Systems

Therichnonlinear dynamics ofchaosallows to modelabroadvariety ofsystems, including complex biological ones. Thesystem ofinterest isusually observed through some timeseries andthemodelling problem consists ofadjusting theparameters ofamodelchaotic system until itsdynamics is matched tothereference timeseries. Inthis paper, wedescribe a general methodology toadaptively select thevalues ofthemodel parameters. Specifically, we assumethattheobserved time series areoriginated byaprimary chaotic system withunknown parameters andweuseittodrive asecondary chaotic system, so thatbothsystem becoupled. Theparameters ofthesecondary system areadaptively optimized byswarmintelligence tomake itfollow thedynamics oftheprimary system. A newapproach toparticle motion inswarmoptimization isdeveloped. Inthis way,thesecondary parameters areinterpreted asestimates of theprimary ones.We illustrate theapplication ofthemethod byjointly estimating thecomplete parameter vector ofaLorenz system.