scholarly journals The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2120
Author(s):  
Jinxiu Pi ◽  
Hui Yang ◽  
Yadong Shu ◽  
Chongyi Zhong ◽  
Guanghui Yang
Keyword(s):  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stable Strategy ◽  
Two Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Evolutionarily Stable

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

scholarly journals Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 431
Author(s):  
Chongyi Zhong ◽  
Hui Yang ◽  
Zixin Liu ◽  
Juanyong Wu
Keyword(s):  
Time Delay ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Games ◽  
Stability Conditions ◽  
Stable Strategy ◽  
Distributed Time Delay ◽  
Player Game ◽  
The Stability ◽  
Evolutionarily Stable

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Stability and Stabilization for Polytopic LPV Systems with Parameter-Varying Time Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Fu Chen ◽  
Shugui Kang ◽  
Fangyuan Li
Keyword(s):  
Time Delays ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Lpv Systems ◽  
Stability And Stabilization ◽  
Parameter Varying ◽  
Conditions Of Stability ◽  
Delay Dependent

In this paper, we deal with the problem of stability and stabilization for linear parameter-varying (LPV) systems with time-varying time delays. The uncertain parameters are assumed to reside in a polytope with bounded variation rates. Being main difference from the existing achievements, the representation of the time derivative of the time-varying parameter is under a polytopic structure. Based on the new representation, delay-dependent sufficient conditions of stability and stabilization are, respectively, formulated in terms of linear matrix inequalities (LMI). Simulation examples are then provided to confirm the effectiveness of the given approach.

Synchronization of Uncertain Neural Networks with H8 Performance and Mixed Time-Delays

2011 ◽  
pp. 1208-1232
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

scholarly journals Fault Detection for Wireless Network Control Systems with Stochastic Uncertainties and Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jie Zhang ◽  
Pengfei Guo ◽  
Ming Lyu ◽  
Hamid Reza Karimi ◽  
Yuming Bo
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Wireless Network ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Network Control ◽  
Linear Matrix ◽  
Network Control Systems ◽  
The Stability ◽  
Stochastic Uncertainties

The fault detection problem is investigated for a class of wireless network control systems which has stochastic uncertainties in the state-space matrices, combined with time delays and nonlinear disturbance. First, the system error observer is proposed. Then, by constructing proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the fault detection observer for the discrete system, and observer gain is also derived by solving linear matrix inequalities. Finally, a simulation example shows that when a fault happens, the observer residual rises rapidly and fault can be quickly detected, which demonstrates the effectiveness of the proposed method.

scholarly journals Stability in Switched Cohen-Grossberg Neural Networks with Mixed Time Delays and Non-Lipschitz Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Huaiqin Wu ◽  
Guohua Xu ◽  
Chongyang Wu ◽  
Ning Li ◽  
Kewang Wang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Activation Functions ◽  
Mixed Time Delays ◽  
Switched Neural Networks ◽  
Exponentially Stable ◽  
The Stability ◽  
Delay Dependent

The stability for the switched Cohen-Grossberg neural networks with mixed time delays andα-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.

scholarly journals New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Hamid Reza Karimi ◽  
Mauricio Zapateiro ◽  
Ningsu Luo
Keyword(s):  
Sufficient Conditions ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Neutral Systems ◽  
Neutral Delay ◽  
Change Of Variables ◽  
Parameter Perturbations ◽  
The Stability ◽  
Delay Dependent

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

Synchronization of Uncertain Neural Networks with performance and Mixed Time-Delays

2011 ◽  
pp. 261-288
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

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