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April  2021, 14(4): 1273-1299. doi: 10.3934/dcdss.2020369

Complex systems with impulsive effects and logical dynamics: A brief overview

1. 

School of Mathematics, Southeast University, Nanjing 210096, China

2. 

School of Information Science and Engineering, Southeast University, Nanjing 210096, China

* Corresponding author: Jianquan Lu

Received  September 2019 Revised  January 2020 Published  April 2021 Early access  May 2020

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.

Citation: Bangxin Jiang, Bowen Li, Jianquan Lu. Complex systems with impulsive effects and logical dynamics: A brief overview. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1273-1299. doi: 10.3934/dcdss.2020369
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Figure 1.  An example of GAII $ T_{ga} = +\infty $
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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