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Related papers: Strange Nonchaotic Attractors in Harper Maps

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In this article, we study a two-parameter family of rotating rank-one maps defined on $\textbf{S}^1\times [1, 1+b]\times \textbf{S}^1$, with $b\gtrsim 0$, whose dynamics is characterised by a coupling of a family of planar maps exhibiting…

Dynamical Systems · Mathematics 2024-08-20 Alexandre A. P. Rodrigues , Bruno F. Gonçalves

We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system…

Chaotic Dynamics · Physics 2009-11-11 K. Thamilmaran , D. V. Senthilkumar , A. Venkatesan , M. Lakshmanan

We show that the recently introduced 0-1 test can successfully distinguish between strange nonchaotic attractors(SNAs) and periodic/quasiperiodic/chaotic attractors, by suitably choosing the arbitrary parameter associated with the…

Chaotic Dynamics · Physics 2015-06-15 R. Gopal , A. Venkatesan , M. Lakshmanan

We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we…

Dynamical Systems · Mathematics 2007-05-23 Feng Rong

This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are…

chao-dyn · Physics 2009-10-31 A. Venkatesan , M. Lakshmanan

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

Chaotic Dynamics · Physics 2021-11-01 Marat Akhmet , Mehmet Onur Fen , Astrit Tola

In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…

Dynamical Systems · Mathematics 2025-05-20 Laura Gardini , Davide Radi , Noemi Schmitt , Iryna Sushko , Frank Westerhoff

Let $\Phi$ be a quasi-periodically forced quadratic map, where the rotation constant $\omega$ is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under $\Phi$) attracting graph of a nowhere continuous…

Dynamical Systems · Mathematics 2015-03-20 Thomas Ohlson Timoudas

We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit…

Dynamical Systems · Mathematics 2009-11-11 Paul Glendinning , Tobias Jaeger , Gerhard Keller

We estimate numerically the regularities of a family of Strange Non--Chaotic Attractors related with one of the models studied in C. Grebogy et al. (1984) (see also G. Keller (1996)). To estimate these regularities we use wavelet analysis…

Dynamical Systems · Mathematics 2016-04-28 Lluís Alsedà , Josep Maria Mondelo , David Romero i Sànchez

The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In…

Dynamical Systems · Mathematics 2007-05-23 Tobias H. Jaeger

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…

Dynamical Systems · Mathematics 2014-12-22 Gabriel Fuhrmann , Maik Gröger , Tobias Jäger

Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…

Dynamical Systems · Mathematics 2015-12-31 Gabriel Fuhrmann

We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental…

Chaotic Dynamics · Physics 2009-11-13 D. V. Senthilkumar , K. Srinivasan , K. Thamilmaran , M. Lakshmanan

This work contains the results from a comprehensive study of a new class of attractors. The attractors in this class are characterized by strong local instability, but they are not uniformly hyperbolic. Rigorous results on their dynamical,…

Dynamical Systems · Mathematics 2007-05-23 Qiudong Wang , Lai-Sang Young

We propose a method to identify and to locate "repellers'' in quasi-periodically forced logistic map (QPLM), using a kind of Morse decomposition of nested attracting invariant sets. In order to obtain the invariant sets, we use an auxiliary…

Chaotic Dynamics · Physics 2014-03-04 Tsuyoshi Chawanya , Takafumi Sakai

We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assumption on the invariance of an attractor. When nonivertible maps in the base are allowed, one can…

Dynamical Systems · Mathematics 2012-12-19 Lluís Alsedà , Michał Misiurewicz

We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors.…

Dynamical Systems · Mathematics 2022-06-15 Telmo Peixe , Alexandre A. Rodrigues

We study quadratic skew-products with parameters driven over piecewise expanding and Markov interval maps with countable many inverse branches, a generalization of the class of maps introduced by Viana. In particular we construct a class of…

Dynamical Systems · Mathematics 2013-04-02 Paulo Varandas

We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the…

Dynamical Systems · Mathematics 2022-01-05 Alexandre A. P. Rodrigues