Directional Invariance and Control Geometry in Bistable Systems (Preprint)

This project hosts the manuscript and computational resources for the study: "Directional Invariance and Control Geometry in Bistable Systems." The paper develops a geometric theory of parameter sensitivity in a class of bistable dynamical systems characterized by multiplicative–additive separation. We prove that, near any non-degenerate equilibrium, the ratio of sensitivities between two control channels becomes directionally invariant. This invariant depends solely on the fixed-point position and the intrinsic structure of the demand function, remains independent of any smooth deformations of the recovery term.