Chaotic Flows with an Independent Amplitude Scaler

Chaotic systems with independent amplitude regulation remain difficult to realize because most existing approaches couple amplitude adjustment with bifurcation parameters, causing simultaneous changes in attractor topology and dynamical behavior. In this work, we propose a new gallery of three-dimensional chaotic flows in which all nonlinear feedback terms are strictly restricted to quadratic forms, and the amplitude is controlled by a single independent amplitude scaler. The proposed architecture enables two fundamentally different regulation modes: total amplitude control, which uniformly rescales the entire attractor, and partial amplitude control, which selectively adjusts the amplitude of partial state variables while maintaining the remaining state-space structure. A systematic dynamical investigation reveals rich nonlinear phenomena, including symmetry breaking, multistability, attractor merging, and prolonged transient chaos. These results demonstrate that the proposed independent amplitude-scaling framework provides not only a simple mechanism for flexible amplitude regulation, but also an effective tool for geometric regulation, coexistence analysis, and the exploration of complex nonlinear phenomena such as multistability and attractor merging in chaos-based engineering systems.