scholarly journals The Asymptotic Behavior in a Nonlinear Cobweb Model with Time Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky
Keyword(s):  
Continuous Time ◽  
Time Delays ◽  
Price Adjustment ◽  
Global Dynamics ◽  
Delay Model ◽  
Cobweb Model ◽  
Switching Curve ◽  
Two Delays ◽  
The Stability ◽  
Straight Lines

We study the effects of production delays on the local as well as global dynamics of nonlinear cobweb models in a continuous-time framework. After reviewing a single delay model, we proceed to two models with two delays. When the two delays are used to form an expected price or feedback for price adjustment, we have a winding stability switching curve and in consequence obtain repetition of stability losses and gains via Hopf bifurcation. When the two delays are involved in two interrelated markets, we find that the stability switching occurs on straight lines and complicated dynamics can arise in unstable markets.

Dynamic Contest Games with Time Delays

2020 ◽  
Vol 22 (03) ◽  
pp. 1950017
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky
Keyword(s):  
Time Scales ◽  
Characteristic Equation ◽  
Continuous Time ◽  
Local Stability ◽  
Time Delays ◽  
Delay Model ◽  
Delayed Information ◽  
Gradient Dynamics ◽  
Special Cases ◽  
Total Effort

Dynamic asymmetric contest games are examined under the assumption that the assessed value of the prize by each agent depends on the total effort of all agents, and each agent has only delayed information about the efforts of the competitors. Assuming gradient dynamics with continuous time scales, first the resulting one-delay model is investigated. Then, assuming additional delayed information about the agents’ own efforts, a two-delay model is constructed and analyzed. In both cases, first the characteristic equation is derived in the general case, and then two special cases are considered. First, symmetric agents are assumed and then general duopolies are examined. Conditions are derived for the local stability of the equilibrium including stability thresholds and stability switching curves.

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

2015 ◽  
Vol 25 (05) ◽  
pp. 1550074 ◽  
Author(s):  
Lingling Zhang ◽  
Jianhua Huang ◽  
Lihong Huang ◽  
Zhizhou Zhang
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Delayed Feedback Control ◽  
Multiple Delays ◽  
Maglev System ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory ◽  
Time Delayed Feedback

This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.

scholarly journals Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 257 ◽  
Author(s):  
B. A. Pansera ◽  
L. Guerrini ◽  
M. Ferrara ◽  
T. Ciano
Keyword(s):  
Continuous Time ◽  
Delay Differential Equations ◽  
Price Competition ◽  
Time Delays ◽  
Equilibrium Points ◽  
Hopf Bifurcations ◽  
Stage Game ◽  
Set Up ◽  
The Stability ◽  
Delay Differential

The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.

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.

Stochastic Stability and Bifurcations of the Singe-Degree-of Freedom System with Two Delays

2013 ◽  
Vol 631-632 ◽  
pp. 1249-1253
Author(s):  
Xue Wen Qin
Keyword(s):  
Dynamical System ◽  
Stochastic Stability ◽  
Time Delays ◽  
Center Manifold ◽  
Degree Of Freedom ◽  
Hopf Bifurcations ◽  
Stochastic Dynamical System ◽  
Two Delays ◽  
Stability And Bifurcations ◽  
The Stability

In this paper, we analyze a singe-degree-of freedom stochastic dynamical system with two time delays. Applying Hale’s reduction approach and stochastic center manifold, the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

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