时滞干扰环状网络的修正函数投影同步及仿真

doi:10.19596/j.cnki.1001-246x.8648

摘要/Abstract

摘要：

为了提高环状网络保密通信的安全性, 分析时滞干扰对环状网络同步的影响。首先根据环状网络的拓扑结构, 构造时变时滞干扰环状网络的数学模型, 然后基于Lyapunov稳定性方法, 设计自适应控制器控制环状网络, 实现无时滞、常时滞和时变时滞干扰环状网络的修正函数投影同步, 说明该自适应控制器具有普适性。通过数值仿真验证了理论分析的正确性, 同时发现时滞干扰会降低环状网络的同步能力, 时滞值越大, 同步能力越差, 实现同步所需的时间越长。

关键词: 环状网络, 时滞干扰, 修正函数投影同步

Abstract:

To improve the security of secret communication in ring networks, we analyze the effect of time delay interference on a ring network synchronization. Firstly, according to the topology of the ring network, the mathematical model of the ring network disturbed by time-varying delay is constructed. Then, based on the Lyapunov stability method, an adaptive controller is designed to control the ring network, and realize the modified function projection synchronization of the ring network with no time-delay, constant-delay and time-varying-delay, which shows that the adaptive controller is universal. At last, the correctness of the theoretical analysis is verified by numerical simulation, and it is found that the synchronization ability of the ring network is reduced by time-delay interference, the greater the delay, the worse the synchronization ability and the longer the time needed to achieve synchronization.

Key words: ring network, time delay disturbance, modified function projective synchronization

李德奎, 毛北行. 时滞干扰环状网络的修正函数投影同步及仿真[J]. 计算物理, 2023, 40(5): 643-652.

Dekui LI, Beixing MAO. Modified Function Projective Synchronization of the Ring Network with Time-delay Disturbance and Its Simulation[J]. Chinese Journal of Computational Physics, 2023, 40(5): 643-652.

图/表 7

图1 环状网络拓扑结构图

Fig.1 Topology structure diagram of ring network

图2 Lü系统的混沌吸引子相图

Fig.2 Chaotic attractor phase diagram of Lü system

图3 时变时滞干扰环状网络的修正函数投影同步误差

Fig.3 Modified function projection synchronization errors of ring network with time-varying delay disturbance

图4 修正函数投影同步的比例函数图

Fig.4 Proportional function diagram of modified function projection synchronization

图5 环状网络各节点和孤立节点的相图(a) 环状网络的各节点的相图; (b) 孤立节点Lü系统的相图

Fig.5 Phase diagrams of all nodes in a ring network and isolated node (a) phase diagrams of all nodes in a ring network; (b) phase diagram of isolated node Lü system

图6 无时滞干扰环状网络的修正函数投影同步误差的轨迹图

Fig.6 The trajectories of the modified function projection synchronization errors of the ring network without time-delay disturbance

图7 常时滞干扰环状网络的修正函数投影同步误差的轨迹图(a) 时滞值为0; (b) 时滞值为0.3; (c)时滞值为2.5; (d) 时滞值为4.8

Fig.7 The trajectories of the modified function projection synchronization errors of the ring network with time-delay disturbance (a) time-delay value is 0; (b) time-delay value is 0.3;(c) time-delay value is 2.5; (d) time-delay value is 4.8

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