The symmetry approach on economic systems

This paper studies the symmetry on the dynamic equations of economic systems. Symmetry group transforms a solution of the equations to other solutions. Thus we can understand the transformational relations among these solutions. Symmetry describes the invariance of the dynamic equations. Then the symmetry provides more information for the inner structure of the economic systems. The complexity of the socioeconomic phenomena is discussed by using dynamic systems with symmetry. For the calculation of the symmetry, the prolongation technique is adopted. This method reformulates the basic problem of finding solutions of differential equations in a more geometrical form which is suited to the investigation of symmetry groups. Some examples of dynamic equations by using symmetry analysis are also illustrated.