Synchronization of Dynamical Systems in Sense of Metric Functionals of Specific Constraints

Abstract

In this chapter, a theory for synchronization of multiple dynamical systerns under specific constraints is developed from a theory of discontinuous dynamical systems. The metric functionals based on specific constraints are proposed to describe the synchronicity of the two or more dynamical systems to such specific constraints. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed through such metric functionals, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint is presented, and the synchronicity of the two systems to multiple specific constraints is investigated as well. The chapter provides a theoretic frame work in or der to control slave systems which can be synchronized with master systems though specific constraints in a general sense.