Analysis of novel 3D chaotic system, hidden coexisting, adaptive control, offset boosting control, and circuit implementation

This study presents the construction of a novel three-dimensional system that includes three unstable points. The system exhibits three key properties. This system is identified as demonstrating chaotic behavior characterized by two nonlinear elements. Control-related issues are subsequently addressed through the design of the adaptive controller. The adaptive control method incorporates considerations for potential parameter uncertainty. Given that only a single state variable is accessible for the development of the feedback controller, it is concluded that one parameter remains entirely unspecified as a result of the employed methodology. The adaptive controller employs principles derived from Lyapunov stability analysis. The system was also shown to contain multiple hidden coexisting states within a specified parameter range. The combined influence of novel features has not yet been monitored in a chaotic system characterized by unstable equilibrium points. An electronic analogue circuit of the novel chaotic system was developed using MultiSIM, thereby demonstrating the practical viability of the mathematical model for circuit implementation.