Generalized Synchronization of Fractional Order Hyperchaotic Lorenz System

Wang, Tianshu; Wang, Xingyuan

doi:10.1142/s021798490902031x

Cited by 19 publications

(10 citation statements)

References 34 publications

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“…In fact, by using the first law of thermodynamics on the horizon, it was proved that the gravitational field equations can be rebuilt in a wide range of theories [10]. The same deductions for cosmological setups [11][12][13][14][15][16][17][18] and braneworld scenarios [19][20][21][22][23][24] are valid. A comprehensive review can be found in Ref.…”

Section: Introductionmentioning

confidence: 93%

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

Moradpour

Sheykhi

2015

Int J Theor Phys

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By bearing the Komar's definition for the mass, together with the entropic origin of gravity in mind, we find the Einstein field equations in (n + 1)-dimensional spacetime. Then, by reflecting the (4+1)-dimensional Einstein equations on the (3+1)-hypersurface, we get the Einstein equations onto the 3-brane. The corresponding energy conditions are also addressed. Since the higher dimensional considerations modify the Einstein field equations in the (3 + 1)-dimensions and thus the energymomentum tensor, we get a relation for the Komar mass on the brane. In addition, the strongness of this relation compared with existing definition for the Komar mass on the brane is addressed.

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Section: Introductionmentioning

confidence: 93%

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

Moradpour

Sheykhi

2015

Int J Theor Phys

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“…Bearing the various definitions of temperature in mind, since the apparent horizon can be considered as the causal boundary, some authors have been shown that the validity of the first law of thermodynamics on the apparent horizon leads to Friedmann equations [40][41][42][43][44][45][46][47][48][49][50][51][52]. In addition, it seems that it is necessary to consider a DE [1,53,54] or modifying the Einstein equations [55] in order to be compatible with recent observations imposing theȧ(t) ≥ 0 and a(t) ≥ 0 conditions on the scale factor [56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic analysis of universes with the initial and final de Sitter eras

2015

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Our aim is studying the thermodynamics of cosmological models including initial and final de-Sitter eras. For this propose, bearing Cai-Kim temperature in mind, we investigate the thermodynamic properties of a dark energy candidate with variable energy density, and show that the state parameter of this dark energy candidate should obey the ωD = −1 constraint, whiles there is no interaction between the fluids filled the universe, and the universe is not in the de-Sitter eras. Additionally, based on thermal fluctuation theory, we study the possibility of inducing fluctuations to the entropy of the dark energy candidate due to a mutual interaction between the cosmos sectors. Therefore, we find a relation between the thermal fluctuations and the mutual interaction between the cosmos sectors, whiles the dark energy candidate has a varying energy density. We point to models in which a gravitationally induced particle production process leads to change the expansion eras, whiles the corresponding pressure is considered as the cause of current acceleration phase. We study its thermodynamics, and show that such processes may also leave thermal fluctuations into the system. We also find an expression between the thermal fluctuations and the particle production rate. Finally, we use Hayward-Kodama temperature to get a relation for the horizon entropy in models including the gravitationally induced particle production process. Our study shows that the first law of thermodynamics is available on the apparent horizon whiles, the gravitationally induced particle production process, as the dark energy candidate, may add an additional term to the Bekenstein limit of the horizon.

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“…It has been found that fractional differential equations can describe many systems in lots interdisciplinary fields. It also has been found that some fractional-order systems demonstrate chaotic and hyperchaotic behavior, such as the fractional-order hyperchaotic Rössler system [8], the fractional-order Chua circuit [9], the fractional-order Lorenz system [10], the fractional-order Liu system [11][12][13] and so on [14,15] .…”

Section: Introductionmentioning

confidence: 99%

Adaptive synchronization of a novel fractional-order hyperchaotic system with uncertain parameters

Yang

Liu

et al. 2015

2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation

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In this paper, the self-synchronization of a new constructed fractional-order hyperchaotic system with uncertain parameters is achieved by the method of adaptive control. Firstly, we proposed a novel fractional-order system which is derived from a integer-order hyperchaotic system. In order to verify the existence of the proposed fractional-order system, numerical simulation and circuitry experimental are carried out. Then to get the self-synchronization of this fractional-order system, adaptive controller is designed according to the stability theory of fractional-order system. By numerical simulation, the correctness and effectiveness of the proposed synchronization method is verified.

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Generalized Synchronization of Fractional Order Hyperchaotic Lorenz System

Cited by 19 publications

References 34 publications

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

Thermodynamic analysis of universes with the initial and final de Sitter eras

Adaptive synchronization of a novel fractional-order hyperchaotic system with uncertain parameters

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