Hopf bifurcation and stability crossing curves in a cobweb model with heterogeneous producers and time delays

Gori, Luca; Guerrini, Luca; Sodini, Mauro

doi:10.1016/j.nahs.2015.06.006

Cited by 25 publications

(26 citation statements)

References 32 publications

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“…We find that the value of the LLE is equal to 0 when τ 1 = 0.2208 in Figure 1b. That is to say, Model (22) appears bifurcation at τ 1 = 0.2208. This is consistent with the conclusion of theoretical analysis.…”

Section: Numerical Simulation and Analysismentioning

confidence: 93%

“…The Influence of τ 1 on the Stability of Equation (22) Model (22) shifts from stable to unstable with the increase of τ 1 , and it has a Hopf bifurcation at Figure 1a shows the dynamic evolution process of Model (22). We can see clearly that energy demand x(t) and energy imports z(t) in east China show an obvious bifurcation.…”

Section: Numerical Simulation and Analysismentioning

confidence: 96%

“…It is easy to get the equilibrium point of Model (22). However, only E(0.8572, 0.4929, 0.6088, 0.1225) conforms to the economic significance.…”

Section: Numerical Simulation and Analysismentioning

confidence: 99%

“…In this case, we consider the characteristic Equation (5) with τ 1 in its stable intervals, i.e., τ 1 ∈ [0, τ 10 ) [22]. We study the impact of τ 2 on the stability of Model (2) when τ 1 unchanged.…”

Section: Local Stability and The Existence Of Hopf Bifurcationmentioning

confidence: 99%

“…Without loss of generality, we assume that Equation (17) has a finite number of positive roots defined by ω 21 , ω 22 , ω 23 , ..., ω 2k , respectively. Fix each ω 2i , (i = 1, 2, ..., k), and there is a series…”

Section: Local Stability and The Existence Of Hopf Bifurcationmentioning

confidence: 99%

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Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Wang

et al. 2016

Entropy

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Abstract:In this paper, a four-dimensional model of energy supply-demand with two-delay is built. The interactions among energy demand of east China, energy supply of west China and the utilization of renewable energy in east China are delayed in this model. We discuss stability of the system affected by parameters and the existence of Hopf bifurcation at the equilibrium point from two aspects: single delay and two-delay. The stability and complexity of the system are demonstrated through bifurcation diagram, Poincare section plot, entropy diagram, etc. in numerical simulation. The simulation results show that the parameters beyond the stable region will cause the system to be unstable and increase the complexity of the system. At this point, because of energy supply-demand system fluctuations, it is difficult to formulate energy policies. Finally, the bifurcation control is realized successfully by the method of delayed feedback control. The results of bifurcation control simulation indicate that the system can return to stable state by adjusting the control parameter. In addition, we find that the bigger the value of the control parameter, the better the effect of the bifurcation control. The results of this paper can provide help for maintaining the stability of the system, which will be conducive to energy scheduling.

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Section: Numerical Simulation and Analysismentioning

confidence: 93%

Section: Numerical Simulation and Analysismentioning

confidence: 96%

“…It is easy to get the equilibrium point of Model (22). However, only E(0.8572, 0.4929, 0.6088, 0.1225) conforms to the economic significance.…”

Section: Numerical Simulation and Analysismentioning

confidence: 99%

Section: Local Stability and The Existence Of Hopf Bifurcationmentioning

confidence: 99%

Section: Local Stability and The Existence Of Hopf Bifurcationmentioning

confidence: 99%

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Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Wang

et al. 2016

Entropy

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Dynamics of a continuous Hénon model

Caraballo

Colucci

Guerrini

2018

Math Methods in App Sciences

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A characterisation of duopoly dynamics with frictions in production adjustments

2017

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This article revisits the classical work of Puu (1991) on duopoly dynamics by gathering\ud two distinct aspects of the functioning of markets: production of goods requires time and\ud is subject to some gestation lags, but trading takes place continuously. Dynamics are\ud characterised by a two-dimensional system of delay differential equations. The main aim\ud of this work is to show that regular and non-regular fluctuations may emerge endogenously\ud because of the existence of heterogeneous interacting agents that choose production period\ud by period in a myopic way. Chaotic dynamics in the discrete-time model of Puu (1991)\ud appear to be close enough to the origin of axes. In contrast, in our continuous-time version\ud of the model with discrete delays, the dynamic system is more suitable of generating\ud complex dynamics far enough from the origin when marginal costs vary. This is because\ud of the role played by time delays and inertia. From a mathematical point of view, we\ud show the existence of Hopf bifurcations and detect how time delays and inertia affect\ud the stability of the system by using the recent techniques of stability crossing curves\ud introduced by Gu et al. (2005) and generalized by Lin and Wang (2012). The article\ud also provides some findings about global bifurcations and chaotic dynamics by combining\ud analytical studies and simulation exercises

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Hopf bifurcation and stability crossing curves in a cobweb model with heterogeneous producers and time delays

Cited by 25 publications

References 32 publications

Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Dynamics of a continuous Hénon model

A characterisation of duopoly dynamics with frictions in production adjustments

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