scholarly journals Bipartite Synchronization of Heterogeneous Signed Networks with Distributed Impulsive Control

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Guizhen Feng ◽  
Jian Ding ◽  
Jinde Cao ◽  
Qingqing Cao
Keyword(s):  
Error Bound ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Mathematical Expression ◽  
Synchronization Error ◽  
Error Level ◽  
Numerical Examples ◽  
Signed Networks ◽  
Average Impulsive Interval ◽  
Theoretical Results

This study investigates the bipartite synchronization of heterogeneous signed networks with distributed impulsive control. Leader-follower bipartite synchronization within a nonzero error bound is analyzed when the average impulsive interval is T a < ∞ or T a = ∞ . Some sufficient conditions to achieve the bipartite quasi-synchronization are presented, and the synchronization error level is estimated by the specific mathematical expression. The correctness of the theoretical results is verified by numerical examples.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

scholarly journals Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chunqing Wu ◽  
Shengming Fan ◽  
Patricia J. Y. Wong
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Studies ◽  
Patchy Environment ◽  
Predator Prey ◽  
Numerical Examples ◽  
Predator Prey Model ◽  
Prey Model ◽  
Dispersal Corridors ◽  
Predator Prey Models ◽  
Theoretical Results

We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey models. By comparing the two permanence criteria, we discuss the effects of dispersal corridors on the permanence of the predator-prey model. It is found that the dispersion of the prey from one patch to another is helpful to the permanence of the prey if the population growth of the prey is density dependent; however, this dispersion of the prey could be disadvantageous or advantageous to the permanence of the predator. Five numerical examples are presented to confirm the theoretical results obtained and to illustrate the effects of dispersal corridors on the permanence of the predator-prey model.

scholarly journals Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chenhui Wang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Numerical Examples ◽  
Mode Synchronization ◽  
Fractional Order Integral

Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.

ROBUST SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

2006 ◽  
Vol 16 (11) ◽  
pp. 3421-3433 ◽  
Author(s):  
XIAOFENG WU ◽  
MUHONG WANG
Keyword(s):  
Frequency Domain ◽  
Error Bound ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
Parameter Mismatch ◽  
Chaotic Lur’E Systems ◽  
Definition Of ◽  
Synchronization Scheme

The sufficient conditions for chaos synchronization of two nonidentical systems by replacing variables control have not been proposed until now. In this paper, synchronization of two chaotic Lur'e systems with parameter mismatch by replacing variables control is studied. First of all, we present a master-slave Lur'e systems synchronization scheme with both parameter mismatch and replacing variables control, and derive a responsive error system for the scheme. A new definition of synchronization with finite L 2-gain is then introduced. Based on the definition, the sufficient synchronization criteria which are in the form of linear matrix inequality (LMI) are proved using a quadratic Lyapunov function. By means of MKY lemma the frequency domain criteria are further derived from the obtained LMIs. These frequency domain criteria are illustrated on the master-slave Chua's circuits with parameter mismatch so that the ranges of the parameters of Chua's circuit are analytically solved in the sense of the synchronization with finite L 2-gain by replacing singe-variable control. The illustrative examples verify that within the ranges of the parameters it is possible to synchronize the master-slave Chua's circuits up to a small synchronization error bound, even the qualitative behaviors of the slave circuit are different from that of the master one, such as the trajectory of the master circuit is chaotic and that of the slave divergent. The relation between the synchronization error bound and parameter mismatch is shown.

On transform orders for largest claim amounts

2021 ◽  
Vol 58 (4) ◽  
pp. 1064-1085
Author(s):  
Yiying Zhang
Keyword(s):  
Lower Bound ◽  
Sufficient Conditions ◽  
Claim Amount ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Numerical Examples ◽  
Comparison Results ◽  
Convex Transform Order ◽  
Star Order ◽  
Theoretical Results

AbstractThis paper investigates the ordering properties of largest claim amounts in heterogeneous insurance portfolios in the sense of some transform orders, including the convex transform order and the star order. It is shown that the largest claim amount from a set of independent and heterogeneous exponential claims is more skewed than that from a set of independent and homogeneous exponential claims in the sense of the convex transform order. As a result, a lower bound for the coefficient of variation of the largest claim amount is established without any restrictions on the parameters of the distributions of claim severities. Furthermore, sufficient conditions are presented to compare the skewness of the largest claim amounts from two sets of independent multiple-outlier scaled claims according to the star order. Some comparison results are also developed for the multiple-outlier proportional hazard rates claims. Numerical examples are presented to illustrate these theoretical results.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

scholarly journals Pinning-controlled synchronization of partially coupled dynamical networks via impulsive control

2022 ◽  
Vol 7 (1) ◽  
pp. 143-155
Author(s):  
Jin Cheng ◽  
Keyword(s):  
Nonlinear Systems ◽  
Communication Channel ◽  
Impulsive Control ◽  
Interval Method ◽  
Channel Matrix ◽  
Outer Synchronization ◽  
Response Systems ◽  
Average Impulsive Interval ◽  
Pinning Impulsive Control ◽  
Theoretical Results

<abstract><p>In this paper, global exponential outer synchronization of coupled nonlinear systems with general coupling matrices are investigated via pinning impulsive control. More realistic and more general partially coupled drive-response systems are established, where the completely communication channel matrix between coupled nodes may not be a permutation matrix. By using pinning impulsive strategy involving pinning ratio and our generalised lower average impulsive interval method, a number of novel and less restrictive synchronization criteria are proposed. In the end, a numerical example is constructed to indicate the effectiveness of our theoretical results.</p></abstract>

scholarly journals Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

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