On the Stability of Input-Output Operators in Nonlinear Systems with Multiple Attractors

We examine the input-output stability of attractors of nonlinear systems to perturbations of finite duration in time. In a low-parameter family of such perturbations, and using techniques from the theory of dynamical systems, we formulate a boundary value problem for the location of critical perturbations, marking the boundary of stability. An intricate pattern of stability and instability is found in a simple illustrative example (the CSTR with a single reaction).