Asymptotic Synchronization Of Partial-state Coupled Systems

In this paper, the asymptotic synchronization in a lattice of partial-state couplednonidentical Lorenz and pendula equations are studied.In Chapter 1, we introduce the background of synchronization including a briefintroduction of nonlinear sciences and the concept of chaotic synchronization.Chapter 2 is devoted to the discussion of the asymptotic synchronization of par-tially coupled Lorenz systems with the external coupling matrices being n×n irreduciblesymmetric real matrices having zero row sums and nonpositive off-diagonal elements.Three different coupling configurations are considered. We first discuss the uniformbounded dissipativeness of the coupled Lorenz systems. Then by Cauchy-Schwarz in-equality we prove that the x_i-coupled and y_i-coupled Lorenz systems asymptoticallysynchronize as long as the coupling streng is large enough. Finally, we show that as-ymptotic synchronization occurs for the coupled Lorenz systems with cross couplingprovided the coupling coefficient is sufficiently large.In Chapter 3, we discuss the asymptotic synchronization of partially coupled non-identical pendula systems. Under the conditions that the external coupling matricesare n×n irreducible symmetric real matrices with zero row sums and nonpositive off-diagonal elements, asymptotic synchronization occurs if the coupling strength exceedsa critical value.Some conclusions and prospects are presented in Chapter 4.