A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan–Yorke dimension and its usage in engineering applications

Designing and analyzing new chaotic systems with desired properties has gotten much interest recently. Through applying modification in a recent rare chaotic flow which has adjustable Kaplan–Yorke dimension, a flexible chaotic system is introduced in this work. In the mentioned modification, two parameters are added which can control amplitude of the attractor and largest Lyapunov exponent. Statistical and dynamical properties of such system could be discovered by applying stability analysis, estimating Lyapunov exponents, local Kaplan–Yorke dimension, and plots of state space. Interestingly, this system is in group of systems which have coexisting attractors, so it is a multistable chaotic system. By considering a practical application of this rare system, meaningful relation between the value of local Kaplan–Yorke dimension and the ability of the system as a random number generator can be seen in statistical tests.