Causodynamics of autowave patterns

Perturbative dynamics of spiral and scroll waves involves the "response functions," i.e., critical eigenvectors of the adjoint linearized operator, dual to the Goldstone modes. A well known method of calculating the Goldstone modes is time integration of the linearized equation. We suggest that backward-time integration of the adjoint linearized equation, which we call causodynamics, can be used to calculate the response functions. This new method is more robust and easier to implement than existing methods. We illustrate how it works for propagating and rotating autowaves in reaction-diffusion systems. The method reveals unexpected qualitative difference between similarly looking regimes.