Ty Partridge, University of Kansas School of Medicine Wichita State University, Wichita, KS

Abstract: Using approach-withdrawal (AW) as a specific instance of temperament, a theoretical model of temperament as a complex dynamic system is proposed. Developmental contextualism (Lerner, 1998) serves as a guiding theory in

Keywords: determining the structural components of the system and Kauffman’s (1993) Boolean models of self-organization are adapted to estimate the parameter functions. In this model P(AW) = f(, ) where P(AW) is the probability density function of an approach or a withdrawal response,  is a standardized parameter estimate of the biological sensitivity to stimulation, and q is a standardized parameter estimate of the contextual response to an approach or withdrawal response. It is theorized that the functions of f and f follow a Hill function of the forms: df /dt = (2/c2 + 2) - K1, d/dt = (2/c2 + 2) - K2, where K1, K2, and c are system constants. This results in a double sigmoid function in which at extreme values of  and  the system stabilizes on a steady state of either approach or withdrawal response patterns. At intermediate parameter values the probability density functions of approach and withdrawal responses are wider. Thus, AW can be modeled as representing two basins of attraction. In addition, considerations are given to the systems sensitivity to initial conditions