Generalized synchronization between Colpitts and Chua circuits

In this contribution, we investigate the Generalized synchronization (GS) problem when we have strictly different nonlinear systems and we consider that for both the slave and master systems only some states are available from measurements. GS in nonlinear systems appears when the states of one system, through a functional mapping are equal to states of another. This mapping can be obtained if there exist a differential primitive element which generates a differential transcendence basis. The first component of the differential transcendence basis is called differential primitive element and, in general, is defined by means of a linear combination of the known states and the control input. Furthermore, we construct a dynamical feedback controller able to achieve complete synchronization in the coordinate transformation systems and GS in the original coordinates. These particular forms of GS are illustrated with numerical results of Colpitts and Chua circuits.