###### Abstract  
Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like bubble, foretells of an imminent bifurcation. With a slight decrease in the gain parameter, we find the symmetric-like bubble changes to a curved trajectory of two equal LEs in one attractor, while an increase in the gain reverses this process in another attractor. We generalize the power-shift method for accessing coexisting attractors or periodic windows by augmenting the technique with an interim parameter shift that optimizes attractor retrieval. We choose the gain as our parameter to interim shift. When interim gain-shift results are compared with LE patterns for a specific gain, we find critical points on the LE spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power shift minimally for large domain attractors. Small domain attractors are less accessible. 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. n +
Footnote †: journal: Applied Sciences  
_Applied Sciences_  
analytical knowledge of the system dynamics. The approach was limited because the feedback loop altered the state variables or system parameters. In 2014, [PERSON] and [PERSON] used amplitude control to detect multistability and coexisting attractors [32]. Later, an offset-boosting-based approach was developed as well for the identification of multistable dynamical systems [33]. [PERSON] et al. [34] developed a power-shift method that changed only the control parameter of the system to transition from one attractor to another. However, the method requires some trial and error. A way to avoid this process may exist in the traditional theoretical tools, for example, the analysis of Lyapunov exponents (LEs), which is discussed further in Section 4.2.1. Lyapunov exponents are able to identify spectral patterns of Hopf bifurcations, period-doubling episodes, tori, and chaos [10; 35]. In 2015 [PERSON] et al. [36] reported that globally analyzed Lyapunov exponents could be used to identify attractor coexistence by comparing forward and backward global scans of the LEs. Lyapunov spectra also predicted the trends of the fundamental frequencies of the output signal of the individual attractors. Structural patterns in the Lyapunov spectra were observed, but the pattern formation was not correlated with the dynamic behavior of the attractor. Later, these specific LE patterns were discovered to predict bifurcation sequences, imminent bifurcations, and common borders of the attractor domains [37]. An imminent bifurcation predicts that by slightly changing a system parameter, one LE pattern changes into another signifying a bifurcation in the system. Herein, we report further findings of pattern formations that predict imminent potential changes in the dynamics provided the gain parameter is modified slightly. We identify the correlation between these LE configurations and the different values of the gain parameter. Specifically, we see an attractor with a curved trajectory of two equal LEs that appears to be benign with respect to its dynamic behavior. A slight increase in the gain produces a symmetric-like bubble whose potential dynamic characteristic is an established pattern identified in Reference [37]. Also, by slightly decreasing the gain of the system, a symmetric-like bubble known to exist in another attractor changes to the curved trajectory of two-equal LEs, just the reverse of the previous attractor event.