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Related papers: Strange non-chaotic attractors in quasiperiodicall…

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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

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked…

Chaotic Dynamics · Physics 2015-06-26 Hinke Osinga , Jan Wiersig , Paul Glendinning , Ulrike Feudel

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

Strange nonchaotic attractors (SNAs) are observed in quasiperiodically driven time--delay systems. Since the largest Lyapunov exponent is nonpositive, trajectories in two such identical but distinct systems show the property of {\it…

Chaotic Dynamics · Physics 2008-02-20 Awadhesh Prasad , Manish Agrawal , Ramakrishna Ramaswamy

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

A simple quasiperiodically forced one-dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors (SNAs) with reference to a two-parameter $(A-f)$ space. The routes include transitions to…

Chaotic Dynamics · Physics 2009-10-31 A. Venkatesan , M. Lakshmanan

Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…

chao-dyn · Physics 2009-10-30 Awadhesh Prasad , Vishal Mehra , Ramakrishna Ramaswamy

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

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

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

The probability distribution of finite-time Lyapunov exponents provides an important characterization of dynamical attractors. We study such distributions for strange nonchaotic attractors (SNAs) created through several different mechanisms…

chao-dyn · Physics 2007-05-23 Awadhesh Prasad , Ramakrishna Ramaswamy

We discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map. This system can have strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors; on SNAs the dynamics is aperiodic,…

Chaotic Dynamics · Physics 2007-05-23 Surendra Singh Negi , Awadhesh Prasad , Ramakrishna Ramaswamy

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I…

chao-dyn · Physics 2016-08-31 Awadhesh Prasad , Vishal Mehra , Ramakrishna Ramaswamy

In this paper, we focus on a numerical technique, the weighted Birkhoff average (WBA) to distinguish between four categories of dynamics for quasiperiodically-forced circle maps. Regular dynamics can be classified by rotation vectors, and…

Chaotic Dynamics · Physics 2025-01-03 E. Sander , J. D. Meiss

We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency…

Dynamical Systems · Mathematics 2020-12-22 Alexandre A. P. Rodrigues

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

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 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

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

We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Henon map. Such dynamics consists in an exponential decay of the radial component and in a…

Chaotic Dynamics · Physics 2007-05-23 Alexey Yu. Jalnine , Sergey P. Kuznetsov , Andrew H. Osbaldestin