Modulatability of complex oscillators

Modulating complex oscillators toward simultaneous multiple spatiotemporal properties is essential for sustaining systems' functionalities. Statistical and dynamical-systems approaches have yielded much progress. However, a comprehensive understanding of modulatability problems, namely, existence and uniqueness of modulation parameters targeting desired properties, remains elusive and challenging. An integrative and efficient framework for identifying those parameters concerning as many properties as possible is also lacking. Here we establish rigorous analyses of modulatability showing that its local-uniqueness condition is generally the equal dimension of parameters and properties. It helps us develop a framework for identifying parameters as a property-based inverse problem, providing an alternative perspective to those trajectory-based methods. The efficacy of the framework is validated across various systems including electronic analogs of genetic circuits. In data-driven demonstrations, our framework achieves less runtime and higher accuracy compared with baseline methods. This work therefore provides rigorous analyses in modulating complex oscillators. Our framework is also a useful tool for future computational and experimental studies.