Parameter estimation of a complex chaotic system with unknown initial values

The parameter estimation of a chaotic system is an important issue in nonlinear science, and it has gained increased attention in recent years. However, the existing estimation methods must be based on the initial values known in the original system. Yet the initial values cannot be obtained in many cases, which is not conducive to the reconstruction and control of chaotic systems. In addition, these methods are unable to provide enough precision for high-dimensional complex chaotic systems. In this paper, a parameter estimation method with unknown initial values is developed, and a new algorithm called the chaos behaved particle swarm optimization algorithm is proposed. Three highlights, namely chaos initialization, special inertia weight and chaos search, are introduced into the algorithm. The simulation experiments are carried out for three complex chaotic systems, including two typical fractional-order hyperchaotic systems and a fractional-order multi-directional multi-scroll chaotic attractor system. Based on the results, the method proposed in this paper demonstrates more effectiveness and advantages than the other four existing algorithms.