一類耦合系統的同步行為

Abstract

在這近幾十年來，耦合系統的同步化行為已經成為相當重要的研究課題。在現有文獻中，用來處理具時間延遲之非線性耦合系統同步化問題的方法仍受到了相當的限制。現有處理非線性藕合系統同步問題的方法大多要求耦合矩陣是與時間無關的、或對稱的，或者要求耦合矩陣之行的總和須為零、或其非對角線元素必須為非負，並且要求耦合函數的斜率必須大於某一個正數。在這個研究中，我們發展出一套可以處理具更一般耦合矩陣形式並具一般形式的耦合函數之具時間延遲的非線性耦合系統的同步化方法。

Synchronization of coupled systems have been important research topics in recent decades. In the literature, the existing methods for the synchronization of nonlinearly coupled systems with delay are still limited. Most of the existing approaches to the synchronization problems of nonlinearly coupled systems require the connectivity matrix to be time-independent, symmetric, with zero row-sums, with nonnegative off-diagonal entries; moreover, these approaches commonly require that the coupling functions have positive lower bounds on their slope. In this project, we develop an approach to the synchronization of nonlinearly coupled systems with delays. Under this approach, the connection matrix could be quite general, and the condition on the slope of the coupling functions, which is commonly imposed on the coupling functions in the existing approaches, is not necessary