scholarly journals Finite-time cluster synchronization of coupled dynamical systems with impulsive effects

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Tianhu Yu ◽  
◽  
Jinde Cao ◽  
Chuangxia Huang ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Impulsive Effects ◽  
Cluster Synchronization

Introduction

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Interconnected Systems ◽  
Large Scale Systems ◽  
Vector Lyapunov Functions ◽  
Finite Time Stabilization ◽  
And Control ◽  
Interconnected Dynamical Systems

This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, with an emphasis on vector Lyapunov function methods and vector dissipativity theory. It examines large-scale continuous-time interconnected dynamical systems and describes thermodynamic modeling of large-scale interconnected systems, along with the use of vector Lyapunov functions to control large-scale dynamical systems. It also discusses finite-time stabilization of large-scale systems via control vector Lyapunov functions, coordination control for multiagent interconnected systems, large-scale impulsive dynamical systems, finite-time stabilization of large-scale impulsive dynamical systems, and hybrid decentralized maximum entropy control for large-scale systems. This chapter provides a brief introduction to large-scale interconnected dynamical systems as well as an overview of the book's structure.

scholarly journals Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents

2010 ◽  
Vol 17 (1) ◽  
pp. 1-36 ◽  
Author(s):  
M. Branicki ◽  
S. Wiggins
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Vector Fields ◽  
Transient Flow ◽  
Time Interval ◽  
Stable And Unstable Manifolds ◽  
Lagrangian Transport ◽  
Transport Barriers ◽  
Unstable Manifolds ◽  
Hyperbolic Trajectories

Abstract. We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of transport barriers in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE) fields and associated Lagrangian coherent structures have been the main tools for characterising transport barriers in the time-aperiodic situation. In this paper we consider a variety of examples, some with explicit solutions, that illustrate in a concrete manner the issues and phenomena that arise in the setting of finite-time dynamical systems. Of particular significance for geophysical applications is the notion of flow transition which occurs when finite-time hyperbolicity is lost or gained. The phenomena discovered and analysed in our examples point the way to a variety of directions for rigorous mathematical research in this rapidly developing and important area of dynamical systems theory.

Adaptive finite-time control for overlapping cluster synchronization in coupled complex networks

2017 ◽  
Vol 266 ◽  
pp. 188-195 ◽  
Author(s):  
Shengqin Jiang ◽  
Xiaobo Lu ◽  
Chao Xie ◽  
Shuiming Cai
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Cluster Synchronization ◽  
Time Control
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