Dynamical models of utility functions for education and health in the Colombian conflict

In this work we develop models of violence and education articulating concepts and methodologies from natural and social sciences. These models serve to analyze the relation between defense and education investment in rural areas of the Colombian national budget between 1950 and 2005, by using nonlinear time series analysis with dynamical systems and economics utility functions. These models determine relations and interdependencies between violence and education consistent with the available empirical information. They also permit to propose alternative ways of evaluating the impact of the public investment in the Colombian conflict, and in general, in the Colombian social development. In order to incorporate both approaches, dynamical systems and utility functions, using nonlinear analysis of time series, we construct dynamical system of coupled differential equations of two state variables corresponding to the utility function of defense and education, and a three dynamical systems where we include the additional public health investment state variable. The construction of the models which describe the temporal evolution of the state variables from the empirical information depends on the considerations of an appropriated complete base of orthonormal functions. The application of extremalization methods from information theory permits to estimate the optimal parameter values without any a priori criteria or any external source of information. This procedure minimizes the complexity of the model using only the empirical information available and reducing the possible introduction of subjective information.