Responses to Constrained Stimulus Sequences in Nonlinear Psychophysics

Generic models used in nonlinear psychophysical dynamics (NPD) have been extensively explored for their capacity to simulate both local singular phenomena and non-monotonic response functions. Internal parameters representing a form of system sensitivity and secondary recursive activity can interact when very low stimulation operates on the gain controlling the evolution of response trajectories, when these trajectories evolve either singly or when chained. Ways in which an existing NPD model can, without change of structure, incorporate naturalistic processes of feedback and stimulus constraint are illustrated. Stimuli-response pairs presented in long closely spaced sequences may appear to be created by a diversity of cognitive strategies, but this assumption is not necessary if nonlinear dynamics are involved. The total system may then resemble the convolution of two fast/slow trajectories. Cusp catastrophe-like sequences can be induced. Nonparametric bases for making statistical comparisons between theory and data, when both are in time series form, are given.