Robert A. M. Gregson, Australian National University, Canberra, Australia

Abstract: The dependency of outputs of three types; real, imaginary and cross-entropy mappings, all over a lattice of pixels, each of which is generated by a complex cubic polynomial nonlinear trajectory, is examined as a function of the crosscoupling between any pixel and its neighbourhood. It is found that the system can transmit information efficiently only within a narrow parameter window, which represents an optimum level of diffusion in space and reconfiguration in time. The topology of stimulus patterns, which are open or closed in their contours, can have a critical effect on the distribution of information in the system's output. Signals which are not processed within a limited temporal and parameter window are eventually degenerated and lost. There are phenomena associated with edge-of-chaos at some stages in the system. Problems of predictability when second-order stochastic noise is superimposed on the trajectory's parameters are explored, and differences from signal detection models are noted.

Keywords: psychophysics, cubic, cross-coupling, edge of chaos, parameter windows