Enhancing Chaotic Resonance in Asymmetric Cubic Maps via Double-Gaussian Asymmetric Feedback

Chaotic resonance can amplify responses of weak external inputs through intrinsic nonlinear fluctuations; however, the effective control of this phenomenon becomes challenging when the attractor dynamics are structurally asymmetric. Building upon preliminary findings, prior studies have investigated whether an asymmetric modification of the double-Gaussian reducing region of the orbit (DG-RRO), allowing independent adjustment of the feedback strength for each branch, could enhance synchronization in asymmetric cubic maps. However, a formalized framework and evaluation under noisy conditions have not yet been provided. In this study, we formalize and extend this concept by introducing an innovative control method called double-Gaussian-asymmetric-filtered reducing-region-of-orbit (DGA-RRO). The DGA-RRO retains the localized, low-intrusiveness filtering of the original DG-RRO while assigning independent Gaussian gains to each side of the orbit, permitting branch-specific tuning and simultaneous attractor-merging bifurcations under pronounced asymmetry. Through systematic numerical experiments across varying asymmetry levels, input amplitudes, frequencies, and two noise models (additive and contaminant), we show that DGA-RRO achieves a higher input–output correlation than symmetric DG-RRO, enables attractor-merging bifurcations to occur under weaker feedback strength, and preserves strong synchronization over a broader parameter range. This method is particularly resilient to contaminant noise and exhibits a well-defined frequency band for optimal performance. These results position the DGA-RRO as a practical extension of earlier asymmetric feedback tests and suggest its applicability to engineering tasks requiring high sensitivity with minimal perturbation, such as neural computation, sensing, and low-power control.