Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model

Wu, Wenjuan; Chen, Zengqiang; Ip, W. H.

doi:10.1016/j.nonrwa.2010.05.022

Cited by 61 publications

(30 citation statements)

References 24 publications

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“…Among this stream of literature, these studies that investigate the dynamic adjustment of players with limited information in competitive settings are most close to our study. Wu et al [30], Ma and Xie [31], and Elsadany [32] studied the evolution processes when the bounded rational players use naive expectation. Considering that players are heterogeneous, some scholars studied the influence of players' different adjustment mechanisms on the dynamics of game model (see [33][34][35][36][37]).…”

Section: Related Literaturementioning

confidence: 99%

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Guo

2017

Complexity

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This paper studies internal reference price effects when competitive firms face reference price effects and make decisions based on partial information, where their decision-making mechanism is modeled by a dynamic adjustment process. It is shown that the evolution of this dynamic adjustment goes to stabilization if both adjustment speeds are small and the complexity of this evolution increases in adjustment speeds. It is proved that the necessary condition for flip bifurcation or Neimark-Sacker bifurcation will occur with the increase of adjustment speed in two special cases. What is more, numerical simulations show that these bifurcations do occur. Then, the impacts of parameters on stability and profits are investigated and some management insights for firms with limited information to take advantage of reference price effects are provided.

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Section: Related Literaturementioning

confidence: 99%

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Guo

2017

Complexity

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“…A revised Kopel oligopoly model with extrapolative foresight was constructed by Gao, Zhong and Mei [11], and Neimark-Sacker bifurcation analysis showed the complex dynamics and the transitions between different dynamical systems. See more research about Kopel oligopoly model in [3,5,10,30,31,35]. As presented above in the related research, dynamical system theory was introduced as an important tool to explore the dynamics in oligopoly theory.…”

Section: Introductionmentioning

confidence: 99%

Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

Chen

2020

Adv Differ Equ

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In this paper, bifurcations and chaotic behaviours of Kopel oligopoly model with different adjustment speed are discussed. The results imply that the Kopel oligopoly model undergoes flip bifurcation, Neimark-Sacker bifurcation, 1:3 and 1:4 resonances, which could induce complex dynamics, especially global behaviours between different orbits. The conditions for the occurrence of three different kinds of bifurcation are derived. Furthermore, the numerical simulations provide us the case study of theoretical analysis and the corresponding dynamical behaviours, especially the occurrence of global orbits.

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“…CHNMS are studied using mathematical modeling based on numerical mathematics and computer graphics, see e.g. [Wu et al, 2010], or on ad hoc methods for specific type of models, see e.g. [Carlettia et al, 2008].…”

Section: Introductionmentioning

confidence: 99%

Qualitative Upper and Lower Approximations of Complex Nonlinear Chaotic and Nonchaotic Models

Dohnal

Doubravský

2015

Int. J. Bifurcation Chaos

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Soft sciences, e.g. economics, ecology, sociology and their various integrations, are often used to develop e.g. forecasting models and optimization constraints. However, highly nonlinear, vague, partially inconsistent and multidimensional systems are prohibitively difficult to study at the quantitative level. Different types of quantitative simplifications are therefore used, e.g. linearization. The resulting models are oversimplified and therefore inapplicable results are often obtained. There are just three values used to quantify qualitative variables and their derivatives: plus/increasing; zero/constant; negative/decreasing. It means that a set of scenarios, i.e. the qualitative solution, is discrete. A qualitative model can be simplified by ignoring some of its equations. The simplified model is less restrictive and gives more scenarios. This set of scenarios is the model's upper approximation. An additional equation makes the model more complex and the resulting set of fewer scenarios is the lower approximation. A qualitative model of dumped oscillations, upper and lower approximations of well-known Lorenz model and a vaguely known five-dimensional bankruptcy model are presented in detail. The upper approximation of the Lorenz set of differential equations has 213 and its lower approximation has 189 scenarios. No a priori knowledge of qualitative models theory is required.

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Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model

Cited by 61 publications

References 24 publications

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

Qualitative Upper and Lower Approximations of Complex Nonlinear Chaotic and Nonchaotic Models

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