Discrete and Continuous Dynamical Systems - S
2021, Volume 14, Issue 4: 1273-1299. Doi: 10.3934/dcdss.2020369
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Complex systems with impulsive effects and logical dynamics: A brief overview
Bangxin Jiang1, ,
Bowen Li2, and
Jianquan Lu1, ,
School of Mathematics, Southeast University, Nanjing 210096, China
School of Information Science and Engineering, Southeast University, Nanjing 210096, China
* Corresponding author: Jianquan Lu
Early access: May 2020
Abstract Full Text(HTML) Figure(6) Related Papers Cited by
In the past decades, complex systems with impulsive effects and logical dynamics have received much attention in both the natural and social sciences. This historical survey briefly introduces relevant studies on impulsive differential systems (IDSs) and logical networks (LNs), respectively. To begin with, we investigate five aspects of IDSs containing fundamental theory, Lyapunov stability, input-to-state stability, hybrid impulses and delay-dependent impulses. Next, we compactly summarize the research status of some problems of LNs including controllability, stability and stabilization, observability and current research. Moreover, some significant applications of proposed results are illustrated. Finally, based on this overview, we further discuss some future work on complex systems with impulsive effects and logical dynamics.
Complex systems,
impulsive effect,
logical network,
stability analysis,
controllability,
observability.
Mathematics Subject Classification: Primary: 34A37, 06E30; Secondary: 93D20, 93B05, 93B07.
Figure 1. An example of GAII $ T_{ga} = +\infty $
Download: Full-size image PowerPoint slide
Figure 2. Behaviors of IDS (13) with initial value $ x_0 = 0.1 $
Figure 3. Behaviors of system (20) with different impulsive gain
Figure 4. Behaviors of System (25) with different values of $ \nu $ and $ h $
Figure 5. Cryptosystem based on impulsive synchronization
Figure 6. Two kinds of configurations for FSRs based on BNs
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Figures(6)
Bangxin Jiang
Bowen Li
Jianquan Lu