In the book Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems by Mariana Haragus, parameter-dependent center manifolds are discussed. Here it is assumed that only the nonlinear term depends on the parameter. I'm interested in the situation where the linear term also depends on the parameter. Unfortunately I'm unable to find literature about this subject. Any good references are welcome.
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$\begingroup$ The usual trick is to add to dfferential equation for the parameter to the system (its derivative is zero), and then use the center manifold theorem for the system without parameters. Are you interested in situations where, for some reason, this simple trick does not work? $\endgroup$– Michael RenardyCommented Feb 14, 2016 at 15:05
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