Classification of Fractal Hyperchaotic Attractors: Phase Space Reconstruction, Lyapunov Exponents and Embedding Dimensions

Abstract

Modified versions of thirty different mathematical models of chaotic systems are considered which are either fractal chaos, strange attractor or hyperchaotic in nature with a view to ascertain the most chaotic system through simulation studies by the computation of their respective Lyapunov exponents and embedding dimensions. The implementation and simulation results show that all of the thirty systems exhibits fractal chaotic behaviour with strange attractor properties while nine out of the thirty exhibit hyperchaotic behaviours. The modification introduced in this study in this paper provides faster convergence properties and non-singularity of the systems considered. Thus, the modified versions can be adapted and deployed for the modelling, prediction and control of highly fractal chaotic, strange attractors and hyperchaotic systems in engineering, financial, biological, management systems, lower and upper atmospheric research, medicine, sciences, etc.