具有时变时滞脉冲的复杂网络同步问题研究

Impulsive complex networks have gained increasing research attention in the past few years due to their wide applications in physics, chemistry, biological, Engineering technology, economics and social science. Due to the mathematical difficulty, synchronization of complex networks with delayed impulsive effects has been largely overlooked. However, in practical situations, for a complex network under impulsive effects, impulsive input delays are necessary to be taken into account because of the finite speed of transmitting signals. Hence,.it becomes desirable to investigate the synchronization of complex networks with delayed impulses. In this project, by means of Gronwall inequality, comparison principle and Lyapunov stability theory, we study the synchronization of complex networks with heterogeneous impulses, time-varying delayed impulses, several criteria will be obtained. Then, we will analyze the effects of impulsive input delay, impulsive strengths and coupling strengths on the synchronization of networks.

脉冲复杂网络由于其在物理、化学、生物、工程技术、经济以及社会科学等领域的广泛应用引起了人们的日益关注。由于数学推导处理的难度，具有时滞脉冲的复杂网络同步问题还很少涉及。然而，真实系统中，脉冲效应在网络中的传输不可避免遭受传输时滞影响。因此研究具有时滞脉冲的复杂网络同步更具研究意义。本项目针对几类具有时滞脉冲的复杂网络系统研究同步问题。采用Gronwall不等式、比较原理 以及Lyapunov 稳定性理论等方法，拟针对具有时滞脉冲的异质复杂网络同步和时变时滞脉冲的复杂网络同步等问题进行深入研究。得到简单可行的判据，从而进一步揭示脉冲传输时滞、脉冲强度以及耦合强度对于网络同步性能的影响。最终，建立一套切实可行的时滞脉冲复杂网络同步研究方法。