Topic

# Rössler attractor

About: Rössler attractor is a research topic. Over the lifetime, 498 publications have been published within this topic receiving 21166 citations.

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TL;DR: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable as mentioned in this paper, which allows for a "folded" Poincare map (horseshoe map).

3,334 citations

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TL;DR: In this article, the same properties can be observed in a simple mapping of the plane defined by: \({x i + 1}} = {y_i} + 1 - ax_i^2,{y i+ 1} = b{x_i}\).

Abstract: Lorenz (1963) has investigated a system of three first-order differential equations, whose solutions tend toward a “strange attractor”. We show that the same properties can be observed in a simple mapping of the plane defined by: \({x_{i + 1}} = {y_i} + 1 - ax_i^2,{y_{i + 1}} = b{x_i}\). Numerical experiments are carried out for a =1.4, b = 0.3. Depending on the initial point (x 0,y 0), the sequence of points obtained by iteration of the mapping either diverges to infinity or tends to a strange attractor, which appears to be the product of a onedimensional manifold.by a Cantor set.

2,507 citations

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TL;DR: In this paper, the authors reported the finding of a chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.

Abstract: This Letter reports the finding of a new chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.

2,443 citations

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TL;DR: This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractsor and represents the transition from one to the other.

Abstract: This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractor and represents the transition from one to the other.

1,655 citations

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TL;DR: In this article, a definition for the concept of "attractor" was proposed based on the probable asymptotic behavior of orbits, and the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.

Abstract: This note proposes a definition for the concept of “attractor,” based on the probable asymptotic behavior of orbits. The definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.

987 citations