Synchronization using linear and nonlinear feedbacks: a comparison

Abstract We compare the efficiency of using a nonlinear function compared to a linear function in the feedback term used to attempt synchronization of two logistic maps. Using a linear function in the feedback term, synchronization is achieved in certain cases when the two systems are operating at identical parameter values. However, for maps operating under different parameter conditions exhibiting a different qualitative behavior (generalized synchronization), linear feedback is successful in attaining only partial synchronization. In comparison, feedback using nonlinear terms is successful in achieving both synchronization and generalized synchronization. Using nonlinear feedback, the dynamics of the response system can be converted from chaotic to periodic (chaos control), from one period to the other and even from periodic to chaotic (chaos anticontrol), depending on the dynamical behavior of the drive system. This is of possible relevance to various systems, where in certain situations the emergence of chaos is undesirable, while under different circumstances loss of the chaotic dynamics corresponds to failure.