Model for hydromagnetic convection in a magnetized fluid

Macek, Wiesław M.; Strumik, M.

doi:10.1103/physreve.82.027301

Cited by 21 publications

(30 citation statements)

References 15 publications

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“…2(a) agrees with the numerically determined blue line in Fig. 2(b) (taken from [Macek & Strumik, 2010] for the same set of control parameters), which presents three regions of different dynamical behaviors (fixed points with no oscillations, or periodic and chaotic dynamics). Let us check the transversality condition at r H values presented in Fig.…”

Section: Hopf Bifurcation In the Generalized Lorenz Modelsupporting

confidence: 82%

“…In the analysis presented here, we focus on the fourdimensional model proposed by Macek and Strumik [2010], which describes the self-consistently convective transport of magnetized fluids. This generalization of the standard Lorenz model [Lorenz, 1963] is expressed by the following equations:…”

Section: Modelmentioning

confidence: 99%

“…Variable X, like in the standard Lorenz model, is proportional to the intensity of the convective motion, Y and Z describe the temperature profile. W is a new time dependent variable, describing the profile of the magnetic field induced in a convected magnetized fluid, see [Macek & Strumik, 2010. The new control parameter ω 0 represents dimensionless magnetic frequency, while σ m = σ/P r m , where P r m is the magnetic Prandtl number.…”

Section: Modelmentioning

confidence: 99%

“…The system (1) has only two nonlinearities, quadratic terms XY and XZ . Besides the origin C 0 = (0, 0, 0, 0), for r ≥ 1 + ω 2 0 σσm , two other nontrivial equilibrium points C ± = (x ± , y ± , z ± , w ± ) exist with [Macek & Strumik, 2010]:…”

Section: Modelmentioning

confidence: 99%

“…In this paper, we analyze the dynamics of the four-dimensional hyperchaotic Lorenz system proposed by Macek and Strumik, where fourth additional variable describes the profile of the magnetic field induced in a convected magnetized fluid [Macek & Strumik, 2010]. The analysis of the largest Lyapunov exponents for this model performed in the frame of papers [Macek & Strumik, 2010 showed that, in general, the system is complex, with periodic, chaotic and hyperchaotic behavior when the control parameters vary [Macek & Strumik, 2014]. Moreover, in the above-mentioned works, authors determined one set of parameters for the generalized Lorenz model, for which type I intermittency appears and there is one place where type III intermittency exists.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Hopf Bifurcations, Periodic Windows and Intermittency in the Generalized Lorenz Model

Wawrzaszek

Krasińska

2019

Int. J. Bifurcation Chaos

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In the present study, we analyze the dynamics of a four-dimensional generalized Lorenz system with one variable describing the profile of the magnetic field induced in a convected magnetized fluid. In particular, we identify the subcritical Hopf bifurcation, at which the dimension of the unstable manifold is increased or reduced by two. Moreover, the new four-dimensional system behavior depending on the control parameters is considered and bidirectional bifurcation structures are revealed. The results show the existence of several windows of nonchaotic variation (windows of order), in particular period-3 windows at the edge of which type I intermittency is observed.

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Section: Hopf Bifurcation In the Generalized Lorenz Modelsupporting

confidence: 82%

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hopf Bifurcations, Periodic Windows and Intermittency in the Generalized Lorenz Model

Wawrzaszek

Krasińska

2019

Int. J. Bifurcation Chaos

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On the Origin of the Universe: Chaos or Cosmos?

Macek

2022

14th Chaotic Modeling and Simulation International Conference

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I would like to consider the Universe according to the standard Big Bang model, including various quantum models of its origin. In addition, using the theory of nonlinear dynamics, deterministic chaos, fractals, and multifractals I have proposed a new hypothesis, Macek (The Origin of the World: Cosmos or Chaos? Cardinal Stefan Wyszyński University (UKSW) Scientific Editions, 2020). Namely, I have argued that a simple but possibly nonlinear law is important for the creation of the Cosmos at the extremely small Planck scale at which space and time originated. It is shown that by looking for order and harmony in the complex real world these modern studies give new insight into the most important philosophical issues beyond classical ontological principles, e.g., by providing a deeper understanding of the age-old philosophical dilemma (Leibniz, 1714): why does something exist instead of nothing? We also argue that this exciting question is a philosophical basis of matters that influence the meaning of human life in the vast Universe.

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