Finding More Chaotic Flows with Complete Control

Chaotic signals play an important role in chaos-based engineering applications; however, signal conditioning is typically required before deployment, necessitating chaos regulation with respect to both amplitude and average values. Therefore, chaotic flows with complete control are of particular importance, which offer significant convenience for chaos-based applications. Complete control implies that the associated chaotic systems can achieve direct chaotic signal rescaling and offset boosting through separate and independent parameter tuning corresponding to distinct components in real circuits. In this work, 16 new candidates of chaotic flows with complete control are systematically identified through exhaustive computer searching combined with algebraic analysis. These systems are classified into two categories, which exhibit partial or total amplitude control combined with offset boosting. The diversity of control mechanisms is further enriched by the introduction of absolute-value nonlinearities, which enable new symmetry properties and robust chaos. Fundamental dynamical analysis, including Lyapunov exponents, Kaplan–Yorke dimensions, equilibrium structures, and bifurcation behaviors, is performed on representative candidates.