Asymptotically exact codimension-four dynamics and bifurcations in two-dimensional thermosolutal convection at high thermal Rayleigh number: Chaos from a quasi-periodic homoclinic explosion and quasi-periodic intermittency

Eilertsen, Justin; Magnan, Jerry F.

doi:10.1016/j.physd.2018.06.004

Cited by 8 publications

(5 citation statements)

References 38 publications

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“…Another important example of a wild hyperbolic attractor is the discrete Lorenz attractor which appears, in particular, in the Poincare maps for periodically perturbed flows with Lorenz attractors 14 . They were also observed in applications, such as the nonholonomic rattleback model 6 and twocomponent convection 5 . It is well-known that the classical Lorenz attractor does not allow homoclinic tangencies 15,16 , however the latter can appear under small non-autonomous periodic perturbations, this is a method to make a wild hyperbolic attractor out of the Lorenz attractor.…”

Section: Introductionmentioning

confidence: 80%

“…where H2,4 (0, µ) = 0, R2 (x, µ) = O( x 2 ). In coordinates (5) 2. By definition, it is a two-dimensional invariant manifold, that is tangent to the leading stable direction (corresponding to λ 1 ) at the saddle point and contains unstable manifold W u (O).…”

Section: Diffeomorphismsmentioning

confidence: 99%

“…For a saddle fixed point O j with eigenvalues λ 1 j , λ 2 j , γ j , |λ 2 j | < |λ 1 j |, the local map can be brought to the main normal form (5). This gives us the following formula for its k-th iteration (see Refs.…”

Section: A Local Mapsmentioning

confidence: 99%

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Global and local bifurcations, three-dimensional Henon maps and discrete Lorenz attractors

Ovsyannikov

2021

Preprint

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Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist in applied models and be observed in experiments. It is known that discrete Lorenz attractors can appear in local and global bifurcations of multidimensional diffeomorphisms. However, to date only partial cases were investigated. In this paper bifurcations of homoclinic and heteroclinic cycles with quadratic tangencies of invariant manifolds are studied. A full list of such bifurcations, leading to the appearance of discrete Lorenz attractors is provided. In addition, with help of numerical techniques, it was proved that if one reverses time in the diffeomorphisms described above, the resulting systems also have such attractors. This result is an important step in the systematic studies of chaos and hyperchaos. a

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Section: Introductionmentioning

confidence: 80%

Section: Diffeomorphismsmentioning

confidence: 99%

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Global and local bifurcations, three-dimensional Henon maps and discrete Lorenz attractors

Ovsyannikov

2021

Preprint

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“…As we know, the first such applied model was a nonholonomic model of Celtic stone [29]. More recently, discrete Lorenz attractors were also found in models of diffusion convection [30,31].…”

Section: Introductionmentioning

confidence: 99%

On discrete pseudohyperbolic attractors of Lorenz type

Gonchenko,

Kazakov

2020

Preprint

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We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors, that can be observed in three-dimensional diffeomorphisms. We propose new phenomenological scenarios of their appearance in one parameter families of such maps. We pay especially our attention to such a scenario that can lead to period-2 Lorenz-like attractors. These attractors have very interesting dynamical properties and we show that their crises can lead, in turn, to the emergence of pseudohyperbolic discrete Lorenz shape attractors of new types. We also show examples of all these attractors in three-dimensional generalized Hénon maps.

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“…They can appear as a result of quite simple bifurcation scenarios [3][4][5]. Therefore, they are encountered in various models from applications, for instance, in the nonholonomic model of a Celtic stone [6,7], in models of diffusion convection [8,9], etc.…”

Section: Introductionmentioning

confidence: 99%

Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps

Kuryzhov¹,

Efrosiniia

Mints

2021

Nelin. Dinam.

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We consider the system of two coupled one-dimensional parabola maps. It is well known that the parabola map is the simplest map that can exhibit chaotic dynamics, chaos in this map appears through an infinite cascade of period-doubling bifurcations. For two coupled parabola maps we focus on studying attractors of two types: those which resemble the well-known discrete Lorenz-like attractors and those which are similar to the discrete Shilnikov attractors. We describe and illustrate the scenarios of occurrence of chaotic attractors of both types.

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Asymptotically exact codimension-four dynamics and bifurcations in two-dimensional thermosolutal convection at high thermal Rayleigh number: Chaos from a quasi-periodic homoclinic explosion and quasi-periodic intermittency

Cited by 8 publications

References 38 publications

Global and local bifurcations, three-dimensional Henon maps and discrete Lorenz attractors

Global and local bifurcations, three-dimensional Henon maps and discrete Lorenz attractors

On discrete pseudohyperbolic attractors of Lorenz type

Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps

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