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对于二维合反应-扩散复杂网络的固定时间同步:边界条件分析.

Yishu Wang1, Jianquan Lu2, Tingwen Huang3

  • 1Department of Public Basic Courses, Nanjing Vocational University of Industry Technology, Nanjing 210023, China.

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概括

本研究为具有冲动和延迟的复杂反应扩散网络建立了固定时间同步 (FxTS) 标准. 拟议的边界控制器确保快速同步,通过数值示例验证.

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科学领域:

  • 复杂的网络 复杂的网络
  • 反应-扩散系统的反应-扩散系统.
  • 控制理论 控制理论

背景情况:

  • 结合反应-扩散复杂网络 (CRDCNs) 对于模拟时空现象至关重要.
  • 在这些网络中实现同步,特别是在冲动和延迟条件下,带来了重大挑战.
  • 固定时间同步 (FxTS) 提供了可取的有限时间融合,而没有有限时间控制的奇点问题.

研究的目的:

  • 在二维合反应扩散复杂网络 (CRDCNs) 中研究和建立固定时间同步 (FxTS) 的标准.
  • 设计有效的边界控制器,保证CRDCN的FxTS受冲动和时间延迟的影响.
  • 分析不同边界条件对同步过程的影响.

主要方法:

  • 利阿普诺夫方法用于确定冲动延迟CRDCN的FxTS标准.
  • 对于设计FxTS边界控制器的Lyapunov-Krasovskii功能方法.
  • 对纽曼,混合和消失的迪里克莱特边界条件的分析.
  • 在正方形域中计算Poincaré不等式的最佳常数.

主要成果:

  • 对于具有同步和非同步冲动和时间延迟的CRDCN,衍生出一种新的FxTS标准.
  • 两个FxTS边界控制器成功为诺伊曼和混合边界条件制定.
  • 已经证明,消失的迪里克莱特边界条件有助于同步.
  • 确定正方形域的最佳普恩卡雷不等式常数,帮助控制器分析.

结论:

  • 拟议的方法有效地在具有挑战条件的复杂反应扩散网络中实现固定时间同步.
  • 开发的边界控制器是强大的和高效的,为同步问题提供了实际的解决方案.
  • 理论发现通过全面的数值模拟得到验证,证实了它们的实际应用.