Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach

Abstract

The arc-length continuation framework is used for the design of state feedback control laws that enable a microscopic simulator trace its own open-loop coarse bifurcation diagram. The steering of the system along solution branches is achieved through the manipulation of the bifurcation parameter, which becomes our actuator. The design approach is based on the assumption that the eigenvalues of the linearized system can be decomposed into two well separated clusters: one containing eigenvalues with large negative real parts and one containing (possibly unstable) eigenvalues close to the origin.

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• Detection of coarse-grained unstable states of microscopic/stochastic systems: a timestepper-based iterative protocol
• A Systems-Based Approach to Multiscale Computation: Equation-Free Detection of Coarse-Grained Bifurcations