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Control of multistable dynamics has important applications, from physics to biology, but the complexity of the systems of differential equations used for their modeling often makes this problem intractable from a global perspective. Here, we propose that for a certain class of multistable dynamical systems, including monotone systems, linearized control at the stable and saddle points of the multistable dynamics can lead to predictable global changes in the relative sizes and depths of its basins of attraction. Our parameter control signal is computationally cheap and provides information about the sensitive parameters to be manipulated in an experimental setting.

Control of Multistability Through Local Sensitivity Analysis: Application to Cellular Decision-Making Networks