A quadratic empirical model formulation for dynamical systems using a genetic algorithm

A new procedure to formulate nonlinear empirical models of a dynamical system is presented. This nonlinear modeling technique generalizes the Markovian techniques used to build linear empirical models, but incorporates a quadratic nonlinearity. The model fit is accomplished using a genetic algorithm. The nonlinear empirical model is applied to two low order model test cases demonstrating different forms of nonlinearity. The two equation predator/prey model (Lotka-Volterra equations) is modeled in the regime of a stable limit cycle. The nonlinear empirical model is able to capture the general shape of the limit cycle, but does not display the long time stability. The second example is the three dimensional Lorenz system forced in the chaotic regime. The general shape and location in phase space of the chaotic attractor is reproduced by the nonlinear empirical model. The results presented here demonstrate that nonlinear empirical models may be able to reproduce some of the nonlinear behaviors of dynamical systems.