14 research outputs found
Controllability of networked multiagent systems based on linearized Turing's model
Turing's model has been widely used to explain how simple, uniform structures
can give rise to complex, patterned structures during the development of
organisms. However, it is very hard to establish rigorous theoretical results
for the dynamic evolution behavior of Turing's model since it is described by
nonlinear partial differential equations. We focus on controllability of
Turing's model by linearization and spatial discretization. This linearized
model is a networked system whose agents are second order linear systems and
these agents interact with each other by Laplacian dynamics on a graph. A
control signal can be added to agents of choice. Under mild conditions on the
parameters of the linearized Turing's model, we prove the equivalence between
controllability of the linearized Turing's model and controllability of a
Laplace dynamic system with agents of first order dynamics. When the graph is a
grid graph or a cylinder grid graph, we then give precisely the minimal number
of control nodes and a corresponding control node set such that the Laplace
dynamic systems on these graphs with agents of first order dynamics are
controllable.Comment: 13 pages, 4 figures, submitted to automatic