Dynamics of Arms Race Model at Fractional Order

Abstract

Mathematical theory of fractional calculus has applied to study many fields of physical science recently. In this paper, this theory has applied further to study on mathematical model of arms race proposed by Saperstein. The model is in the discrete form of couple logistic equations. This type of dynamical system may provide key to understand complex behaviors in social and political science in term of nonlinear dynamics. The conflict event that leads to outbreak of war can be identified as the transition to chaotic state in dynamical system. The dynamical behaviors of the arms race model explain by phase space. The numerical calculations of the arms race model have presented their fractional-order state behaviors.