scholarly journals Synchronization conditions in networks of Hindmarsh-Rose systems

2021 ◽  
pp. 254-259
Author(s):  
Sergei A. Plotnikov
Keyword(s):  
Function Method ◽  
Sufficient Condition ◽  
Algebraic Connectivity ◽  
Simple Condition ◽  
Neuron Models ◽  
Individual System ◽  
Lyapunov Function Method ◽  
Coupled Networks ◽  
The Individual ◽  
Crucial Parameter

The algebraic connectivity is crucial parameter in studying of synchronization of diffusively coupled networks. This paper studies the synchronization in networks of Hindmarsh-Rose systems, which is one of the most used neuron models. It presents sufficient condition for synchronization in these networks using the Lyapunov function method. This is a simple condition which depends on the algebraic connectivity and on the parameters of the individual system. Numerical examples are presented to illustrate the obtained results.

scholarly journals Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1663
Author(s):  
Yiqing Xue ◽  
Ping Zhao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
State Feedback ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Stability And Stabilization

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results.

scholarly journals ON A FABRIC OF KISSING CIRCLES

2021 ◽  
pp. 1-10
Author(s):  
VIERA ČERŇANOVÁ
Keyword(s):  
Sufficient Condition ◽  
Arithmetic Sequence ◽  
Square Grid ◽  
The Individual

Abstract Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

Fast Finite-Time Consensus Tracking of First-Order Multi-Agent Systems with a Virtual Leader

2014 ◽  
Vol 596 ◽  
pp. 552-559 ◽  
Author(s):  
Qiu Yun Xiao ◽  
Zhi Hai Wu ◽  
Li Peng
Keyword(s):  
Graph Theory ◽  
Finite Time ◽  
Function Method ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
First Order ◽  
Consensus Tracking ◽  
Lyapunov Function Method ◽  
Multi Agent ◽  
Virtual Leader

This paper proposes a novel finite-time consensus tracking protocol for guaranteeing first-order multi-agent systems with a virtual leader to achieve the fast finite-time consensus tracking. The Lyapunov function method, algebra graph theory, homogeneity with dilation and some other techniques are employed to prove that first-order multi-agent systems with a virtual leader applying the proposed protocol can reach the finite-time consensus tracking. Furthermore, theoretical analysis and numerical simulations show that compared with the traditional finite-time consensus tracking protocols, the proposed protocol can accelerate the convergence speed of achieving the finite-time consensus tracking.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

CHAOS SYNCHRONIZATION VIA UNIDIRECTIONAL COUPLING AND ITS APPLICATION TO SECURE COMMUNICATION

2009 ◽  
Vol 23 (32) ◽  
pp. 5949-5964 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Function Method ◽  
The Self ◽  
Largest Lyapunov Exponent ◽  
Global Synchronization ◽  
Unidirectional Coupling ◽  
Response System ◽  
Lyapunov Function Method ◽  
Simulation Results

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method.

scholarly journals Independent of delay stabilization using implicit Lyapunov function method

Automatica ◽  
2019 ◽  
Vol 101 ◽  
pp. 103-110
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Lyapunov Function Method

scholarly journals Community Global Observing System Simulation Experiment (OSSE) Package (CGOP): Assessment and Validation of the OSSE System Using an OSSE–OSE Intercomparison of Summary Assessment Metrics

2018 ◽  
Vol 35 (10) ◽  
pp. 2061-2078 ◽  
Author(s):  
Sid-Ahmed Boukabara ◽  
Kayo Ide ◽  
Yan Zhou ◽  
Narges Shahroudi ◽  
Ross N. Hoffman ◽  
...  
Keyword(s):  
System Simulation ◽  
Weather Prediction ◽  
Real Data ◽  
New Techniques ◽  
Forecast Performance ◽  
Individual System ◽  
Assessment Metrics ◽  
The Individual ◽  
The Tropics ◽  
Observing System Simulation Experiment

AbstractObserving system simulation experiments (OSSEs) are used to simulate and assess the impacts of new observing systems planned for the future or the impacts of adopting new techniques for exploiting data or for forecasting. This study focuses on the impacts of satellite data on global numerical weather prediction (NWP) systems. Since OSSEs are based on simulations of nature and observations, reliable results require that the OSSE system be validated. This validation involves cycles of assessment and calibration of the individual system components, as well as the complete system, with the end goal of reproducing the behavior of real-data observing system experiments (OSEs). This study investigates the accuracy of the calibration of an OSSE system—here, the Community Global OSSE Package (CGOP) system—before any explicit tuning has been performed by performing an intercomparison of the OSSE summary assessment metrics (SAMs) with those obtained from parallel real-data OSEs. The main conclusion reached in this study is that, based on the SAMs, the CGOP is able to reproduce aspects of the analysis and forecast performance of parallel OSEs despite the simplifications employed in the OSSEs. This conclusion holds even when the SAMs are stratified by various subsets (the tropics only, temperature only, etc.).

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