Hopf bifurcations in a Ricardo-Malthus model

Zhou, Ming-Chun; Liu, Zongyu

doi:10.1016/j.amc.2010.07.043

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Existence of this bifurcation in system (1) is analytically studied in [2], but this work presents numerical existence. is varied, and it is easy to see that before Hopf bifurcation 6 is stable and the system can converge to it in the long run depending on initial condition.…”

Section: A Andronov-hopf Bifurcationmentioning

confidence: 98%

Non-linear and non-smooth dynamics in a sustainable development system

Olivar

Amador

2011

2011 IEEE Second Latin American Symposium on Circuits and Systems (LASCAS)

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This paper presents the dynamic interaction between natural resource and population, and also introduce technological progress as an extra dynamic equation. Hopf, saddlenode, and two-parameter bifurcation were found in the planar system, and chaotic behaviour appeared in the 3D system. Nonsmooth phenomena such as sliding and stable pseudo equilibrium appeared when smooth systems were replaced by non-smooth system.

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Section: A Andronov-hopf Bifurcationmentioning

confidence: 98%

Non-linear and non-smooth dynamics in a sustainable development system

Olivar

Amador

2011

2011 IEEE Second Latin American Symposium on Circuits and Systems (LASCAS)

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“…Since matrix J have one real eigenvalue which is smaller than zero and a pair of complex conjugate eigenvalues, Hopf bifurcation may emerge in (4) [10][11][12][13][14][15][16][17][18][19]. We will investigate the bifurcation using invariant manifold in dynamical systems.…”

Section: Analysis Of the Modelmentioning

confidence: 99%

Dynamical behavior of a competition model of Telcom and Cable Television industry

Fan

Zhang

2011

Nonlinear Dyn

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Under the trend of the integration of the Internet, Telcom, and Cable Television (CATV) in China, the penetration and integration in the service of CATV industry and telecom industry will be conducted. With its service changing from the original single video transmission to the diverse communication service, the CATV industry will transform its development plan, thus the adjustment of its developmental strategies. From the influence of the involvement of the three telecommunication operators in Internet Protocol Television (IPTV) on CATV industry and the mutual competitive relationship among them, an analysis of the operating enterprises of the two industries was made by using differential equations. The results show that, under some conditions, one operator in the telecom industry will monopolize the market. And under other conditions, market share of the three operators in IPTV will change periodically.

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“…The work of Malthus [10] and Verhulst [13] is the base to the field of the growth and decline of a population [3,16]. In the nature, species do not exist alone.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a two teams prey-predator interaction model

Aly¹,

Elettreby²

2015

Miskolc Math Notes

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Abstract. In this paper, a model of two teams of predators interacting with two teams of preys is proposed. The predator teams help each other and so do the prey teams. Therefore, some stability analysis are carried out on the model to detect the stability and instability of the system's equilibrium solutions. Also, the persistence of the solutions is investigated. Finally, the optimal control is applied to the unstable equilibrium solutions. Some numerical simulations are carried out to verify the analytic results.2010 Mathematics Subject Classification: 34C23; 35K57; 92D25; 92D30

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Hopf bifurcations in a Ricardo-Malthus model

Cited by 6 publications

References 14 publications

Non-linear and non-smooth dynamics in a sustainable development system

Non-linear and non-smooth dynamics in a sustainable development system

Dynamical behavior of a competition model of Telcom and Cable Television industry

Optimal control of a two teams prey-predator interaction model

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