scholarly journals Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xinlei Yi ◽  
Wenlian Lu ◽  
Tianping Chen
Keyword(s):  
Reaction Dynamics ◽  
Largest Lyapunov Exponent ◽  
Sufficient Condition ◽  
Time Varying ◽  
Complete Synchronization ◽  
Coupling Matrix ◽  
Differential Systems ◽  
General Sufficient Condition ◽  
Theoretical Results ◽  
Ordinary Differential Equation Systems

We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. Inspired by our previous paper (Lu et al. (2007-2008)), the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness of the theoretical results.

GLOBAL SYNCHRONIZATION IN AN ARRAY OF LINEARLY COUPLED DELAYED NEURAL NETWORKS WITH AN ARBITRARY COUPLING MATRIX

2006 ◽  
Vol 16 (11) ◽  
pp. 3357-3368 ◽  
Author(s):  
HONGTAO LU ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Output Coupling ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Delayed Neural Networks ◽  
Arbitrary Coupling ◽  
General Sufficient Condition ◽  
Theoretical Results

In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results.

scholarly journals Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

2012 ◽  
Vol 17 (2) ◽  
pp. 210-222 ◽  
Author(s):  
Xiu Liu ◽  
Shouming Zhong ◽  
Xiuyong Ding
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Functionals ◽  
Sufficient Condition ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Numerical Example ◽  
Impulsive Switched Systems ◽  
Theoretical Results

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

scholarly journals Synchronization of Intermittently Coupled Dynamical Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Gang Zhang ◽  
Guanrong Chen
Keyword(s):  
Coupling Strength ◽  
Stability Theory ◽  
Lorenz System ◽  
Impulsive Differential Equations ◽  
Time Varying ◽  
Coupling Matrix ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
The Stability ◽  
Theoretical Results

This paper investigates the synchronization phenomenon of an intermittently coupled dynamical network in which the coupling among nodes can occur only at discrete instants and the coupling configuration of the network is time varying. A model of intermittently coupled dynamical network consisting of identical nodes is introduced. Based on the stability theory for impulsive differential equations, some synchronization criteria for intermittently coupled dynamical networks are derived. The network synchronizability is shown to be related to the second largest and the smallest eigenvalues of the coupling matrix, the coupling strength, and the impulsive intervals. Using the chaotic Chua system and Lorenz system as nodes of a dynamical network for simulation, respectively, the theoretical results are verified and illustrated.

A NEW COMPARISON METHOD FOR STABILITY THEORY OF DIFFERENTIAL SYSTEMS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 169-186 ◽  
Author(s):  
ZHIGANG ZENG ◽  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Equilibrium Points ◽  
Original System ◽  
Comparison Method ◽  
Delay Systems ◽  
Time Varying ◽  
Convergence Region ◽  
Differential Systems ◽  
Time Varying Delay ◽  
Exponentially Stable ◽  
Theoretical Results

In this paper, a new comparison method is developed by using increasing and decreasing mechanisms, which are inherent in time-delay systems, to decompose systems. Based on the new method, whose expected performance is compared with the state of the original system, some new conditions are obtained to guarantee that the original system tracks the expected values. The locally exponential convergence rate and the convergence region of the polynomial differential equations with time-varying delays are also investigated. In particular, the comparison method is used to improve the 3/2 stability theorems of differential systems with pure delays. Moreover, the comparison method is applied to identify a threshold, and to consider the disease-free equilibrium points of an HIV endemic model with stages of progress to AIDs and time-varying delay. It is shown that if the threshold is smaller than 1, the equilibrium point of the model is globally, exponentially stable. Another application of the comparison method is to investigate the global, exponential stability of neural networks, and some new theoretical results are obtained. Numerical simulations are presented to verify the theoretical results.

scholarly journals Formation Control of Second-Order Multiagent Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hong Xia ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao ◽  
Jun-Yan Yu
Keyword(s):  
Control Problem ◽  
Multiagent Systems ◽  
Formation Control ◽  
Second Order ◽  
Sufficient Condition ◽  
Time Varying ◽  
Consensus Protocol ◽  
Leader Following ◽  
Multiple Leaders ◽  
Theoretical Results

A formation control problem for second-order multiagent systems with time-varying delays is considered. First, a leader-following consensus protocol is proposed for theoretical preparation. With the help of Lyapunov-Krasovskii functional, a sufficient condition under this protocol is derived for stability of the multiagent systems. Then, the protocol is extended to the formation control based on a multiple leaders’ architecture. It is shown that the agents will attain the expected formation. Finally, some simulations are provided to demonstrate the effectiveness of our theoretical results.

scholarly journals Leader-Following Consensus in Networks of Agents with Nonuniform Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhao-Jun Tang ◽  
Ting-Zhu Huang ◽  
Jiang-Ping Hu ◽  
Jin-Liang Shao
Keyword(s):  
Sufficient Condition ◽  
Time Varying ◽  
Consensus Problem ◽  
Communication Delays ◽  
Necessary And Sufficient Condition ◽  
Leader Following ◽  
Fixed Topology ◽  
Simulation Results ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper is concerned with a leader-following consensus problem for networks of agents with fixed and switching topologies as well as nonuniform time-varying communication delays. By employing Lyapunov-Razumikhin function, a necessary and sufficient condition is derived in the case of fixed topology, and a sufficient condition is obtained in the case when the interconnection topology is switched and satisfies certain condition. Simulation results are provided to illustrate the theoretical results.

scholarly journals Design of robust controller for linear systems with Markovian jumping parameters

1998 ◽  
Vol 4 (4) ◽  
pp. 269-288 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas ◽  
O. L. V. Costa ◽  
P. Shi
Keyword(s):  
Linear Systems ◽  
Sufficient Condition ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Robust Controller ◽  
Markovian Jumping ◽  
Stochastic Stabilizability ◽  
Uncertain Linear Systems ◽  
Complete Access ◽  
Theoretical Results

This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals Private and rateless adaptive coded matrix-vector multiplication

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rawad Bitar ◽  
Yuxuan Xing ◽  
Yasaman Keshtkarjahromi ◽  
Venkat Dasari ◽  
Salim El Rouayheb ◽  
...  
Keyword(s):  
Computing Methods ◽  
Erasure Codes ◽  
Time Varying ◽  
New Paradigm ◽  
Matrix Vector Multiplication ◽  
Processing Data ◽  
Computationally Intensive ◽  
Matrix Vector ◽  
Monitoring Devices ◽  
Theoretical Results

AbstractEdge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive tasks by employing erasure codes and offloading these tasks to other devices for computation. Coded computation is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account (1) the privacy requirements of IoT applications and devices, and (2) the heterogeneous and time-varying resources of edge devices. We show that PRAC outperforms known secure coded computing methods when resources are heterogeneous. We provide theoretical guarantees on the performance of PRAC and its comparison to baselines. Moreover, we confirm our theoretical results through simulations and implementations on Android-based smartphones.

Sign in / Sign up

Export Citation Format

Share Document