The extended return map: a new method to analyze the nonlinear dynamics of inter-response-intervals in Skinner-box experiments Jay-Shake Li and Joseph. P. Huston University of Düsseldorf, Germany We modified the so-called “return map”, a method for analyzing a special kind of time series data such as the inter-response-intervals (IRIs) recorded in a Skinner-box experiment. We called this modified version: “extended return map”. For a two-dimensional drawing, the original version of return map is a plot of present data I(t) against the next one I(t+1). The two-dimensional drawing of the extended return map is a plot of summation of L data: [I(t) + I(t+1) +...+ I(t+L-1)] against summation of the next L data: [I(t+L) + I(t+L+1) +...+ I(t+2L-1)]. Here I(t) is the t-th IRIs recorded in the experiment; L is a new parameter we introduced which charac-terizes the features of the extended return map. We call L the “fold” of the extended return map. While the original version of return map applied in Skinner-box experiments on rats showed stochastically distributed points, the extended return map showed clearly identifiable structures. The summation step in our new method works like a low pass filter. The short-term fluctuations in the time series data are suppressed, thus enhancing the long-term changes. Keywords: nonlinear dynamics, Skinner-box, return map

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