Inverse system of general anticipating response scheme

The general anticipating response scheme is a unidirectionally coupled dynamical system. In this paper, in order to achieve the inverse transformation of the signal transformation that the general anticipating response scheme realizes, a cascaded inverse system design method is presented for this scheme. There is a function to be determined in the general anticipating response scheme. According to the chosen function, various specific coupled dynamical systems can be constructed. Accordingly, there is a corresponding function to be determined in the cascaded inverse system, which makes the structure of the inverse system change with the one of the general anticipating response system. In addition, this cascaded inverse system, together with the general anticipating response system, composes a lattice of continuous-time oscillators with three lattice elements. For this lattice, the first and the third elements oscillate completely synchronously while the second one anticipates them. By generalizing this lattice properly, lattices of continuous-time oscillators which have more lattice elements and exhibit richer dynamical behaviors can be constructed, so the work of this paper provides methods and models for constructing and studying lattices of continuous-time oscillators.