## 5 Conclusions  
By power shifting, we can discover windows and access many attractors reliably even with noise on the frequency and a linear ramp on the injected signal amplitude of LIS. We select a base attractor which enhances the power shift's reliability of accessing a desired attractor. Using the modified power-shift technique with the interim parameter shift, we expand access to attractors by temporarily modulating the gain (parameter), in this case. The power-shift method in conjunction with the interim parameter shift is attractive because it can be experimentally applied without significant or long-lasting modifications to the experimental system itself. When gain-shift results are compared to the LE patterns for a specific gain, we find critical points of the spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power-shift technique minimally for large domain attractors. Small domain attractors are inaccessible. Experimentally, we believe that the enhanced power-shift method, which enables an experimentalist to both discover and access coexisting attractors, is appealing because this provides flexibility to move from one type of system dynamics to another. By varying other system parameters, this method could facilitate, for example, a mapping of the dynamical states in parameters space of frequency detuning [7].  
The Lyapunov exponents continue to herald system dynamics, attractor and window domains, and the level of instability associated with the various patterns. We know, for example, that every attractor has a unique LE pattern that is choreographed by the subtle variations of the attractor dynamics and are circumscribed by converging and diverging LE spectral patterns including the signature two-zero LEs at the origin and demise of the attractor [37]. We understand symmetric-like and asymmetric bubbles as imminent bifurcations and existing bifurcations, respectively. These results reiterate the universality of the LEs spectra patterns. There are still unknown patterns observed in other nonlinear systems which need to be defined that may or may not be associated with the LIS systems, but what we do know, is that the Lyapunov spectra has many mysteries yet to be discovered.  
The power-shift method, along with the interim gain shift, is an answer to the question of how to access individual attractors stably and accurately even under experimental conditions. Identifying the dominance of one attractor over another in the same system and understanding the conditions that might change this dominance remains an open issue.  
Figure 15: Schematic of LEs vs \(Y\) graphed over the partial LE domain of AIII at \(C=3.1\) and overlayed with the gain-shift results. The right ordinate displays the percentage that AIII survives the gain shift.  
**Author Contributions:** Conceptualization, J.R.H., E.K.T.B., D.M.C. and D.K.B.; methodology, E.K.T.B., J.R.H.; Software, D.M.C., E.K.T.B., J.R.H.; Data Curation, E.K.T.B., J.R.H. and D.M.C.; writing--original draft preparation, D.K.B.; writing--review and editing, E.K.T.B., J.R.H., D.M.C. and D.K.B.; Visualization, J.R.H.; Supervision, D.K.B. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The APC was funded by MDPI AG.  
**Data Availability Statement:** Data available on request. The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** We are grateful to [PERSON] for his experimental acumen and consultations. We thank [PERSON] and [PERSON] for their valuable computations.  
**Conflicts of Interest:** The authors declare no conflict of interest.