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

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

2003-02-03

arxiv.org/abs/nlin/0302005v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

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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