Nonlinear dynamics of intimate partner violence

Based on the psychological theory of the cycle of violence, we have developed a four discrete states model: -1 passivity, 0 normality, 1 tension, 2 physical assault. Defining the transition matrix and the initial state and parameters of the couple, simulations were run to find the effects of aggression parameter on the payoffs and status in the couple. From the analysis of the phase diagram, depending on the values of the aggressor parameters of the agents the couple, we observed different probabilities of ending up in four absorbing states. These trends are in agreement with the literature data of the IPV.