LYAPUNOV SPECTRUM ANALYSIS AND NUMERICAL CHARACTERISATION OF A NEW FOUR-DIMENSIONAL NONLINEAR SYSTEM
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Abstract
In this work we introduce a new nonlinear autonomous system in four dimensions that includes quadratic interactions and possesses a one-parameter family of equilibrium points. A comprehensive numerical investigation of the Lyapunov spectrum of this system is carried out. To this end, a Benettin–Wolf type algorithm with periodic QR reorthonormalization is implemented to approximate all Lyapunov exponents and the corresponding Kaplan–Yorke dimension.
Over a broad range of parameter values, the system displays chaotic dynamics characterized by a positive largest exponent and an attractor whose effective dimension slightly exceeds two. The reliability of the numerical procedure is assessed by examining its sensitivity to the integration step, the length of the discarded transient, and the renormalization interval. Parameter-dependent plots of the Lyapunov exponents and the Kaplan–Yorke dimension are then used to single out parameter regions where the chaotic behavior is more pronounced. The proposed model and computational routine are finally compared with existing four-dimensional systems and Lyapunov exponent methods, and possible uses in secure communications and image encryption are briefly outlined.