On the stability of quadratic dynamics in discrete time n-player Cournot games

Automatica ◽  
2012 ◽  
Vol 48 (6) ◽  
pp. 1182-1189 ◽  
Author(s):  
Hamed Kebriaei ◽  
Ashkan Rahimi-Kian
Keyword(s):  
Discrete Time ◽  
The Stability ◽  
Cournot Games

scholarly journals On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
The Stability

General lemma for the stability analysis of discrete-time adaptive control

1990 ◽  
Vol 51 (2) ◽  
pp. 283-288 ◽  
Author(s):  
FOUAD GIRI ◽  
MOHAMED M'SAAD ◽  
JEAN-MICHEL DION ◽  
LUC DUGARD
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Discrete Time ◽  
General Lemma ◽  
The Stability

ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK

2016 ◽  
Vol 46 (3) ◽  
pp. 747-778 ◽  
Author(s):  
Lin Yang ◽  
Athanasios A. Pantelous ◽  
Hirbod Assa
Keyword(s):  
Discrete Time ◽  
Regime Switching ◽  
Structural Changes ◽  
Linear Matrix ◽  
H Infinity Control ◽  
R Process ◽  
The Stability ◽  
Markovian Regime Switching ◽  
Markovian Regime

AbstractThe premium pricing process and the medium- and long-term stability of the reserve policy under conditions of uncertainty present very challenging issues in relation to the insurance world. Over the last two decades, applications of Markovian regime switching models to finance and macroeconomics have received strong attention from researchers, and particularly market practitioners. However, relatively little research has so far been carried out in relation to insurance. This paper attempts to consider how a linear Markovian regime switching system in discrete-time could be applied to model the medium- and long-term reserves and the premiums (abbreviated here as the P-R process) for an insurer. Some recently developed techniques from linear robust control theory are applied to explore the stability, stabilisation and robust H∞-control of a P-R system, and the potential effects of abrupt structural changes in the economic fundamentals, as well as the insurer's strategy over a finite time period. Sufficient linear matrix inequality conditions are derived for solving the proposed sub-problems. Finally, a numerical example is presented to illustrate the applicability of the theoretical results.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

scholarly journals Generalized conditions for coexistence of competing parasitoids on a shared host

2020 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Discrete Time ◽  
Life Histories ◽  
Host Density ◽  
Host Community ◽  
Reproduction Rate ◽  
Parasitoid Species ◽  
Slow Increase ◽  
Time Formalism ◽  
Adult Parasitoid ◽  
The Stability

AbstractMotivated by the univoltine life histories of insects residing in the temperate-regions of the world, there is a rich tradition of modeling arthropod host-parasitoid interactions using a discrete-time formalism. We introduce a general class of discrete-time models for capturing the population dynamics of two competing parasitoid species that attack the same vulnerable stage of the host species. These models are characterized by two density-dependent functions: an escape response defined by the fraction of hosts escaping parasitism; and a competition response defined by the fraction of parasitized hosts that develop into adult parasitoids of either species. Model analysis reveals remarkably simple stability conditions for the coexistence of competing parasitoids. More specifically, coexistence occurs, if and only if, the adult host density increases with host reproduction rate, and the log sensitivity of the competition response is less than half. The latter condition implies that any increase in the adult parasitoid density will result in a sufficiently slow increase in the fraction of parasitized hosts that develop into parasitoids of that type. We next consider a model motivated by differences in parasitism risk among individual hosts with risk from the two parasitoid species assumed to be independently distributed as per a Gamma distribution. In such models, the heterogeneity in host risk to each parasitoid is quantified by the corresponding Coefficient of Variation (CV). Our results show that parasitoid coexistence occurs for sufficiently large reproduction rate, if and only if, the sum of the inverse of the two CV squares is less than one. This result generalizes the “CV greater than one” rule that defined the stability for a single parasitoid-host system to a multi parasitoid-host community.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

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