Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure

Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potential

We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural two-dimensional Hamiltonians is presented. The relations with SUSY quantum mechanics are discussed.Comment: 11 pages, Late

Controlling Physical Systems with Symmetries

Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are determined by the irreducible representations of the symmetry group of the linearization about the orbit to be controlled. We use the general results to demonstrate the effect of symmetry on the control of two sample physical systems: a coupled map lattice and a particle in a symmetric potential.Comment: 6 page

A pantropical population genetics study on cashew crop: uncovering genetic diversity and agrobiodiversity hotspots

XIX ENBE Annual Meeting of the Portuguese Association for Evolutionary Biology, 18-19 December 2023, Lisboninfo:eu-repo/semantics/publishedVersio

Molecular assessment of cashew diversity unravels distinctive differentiation routes in CPLP countries

Comunicação OralN/

Fractalization of Torus Revisited as a Strange Nonchaotic Attractor

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon request):submitted to Phys.Rev. E (1996

Simple nonlinear models suggest variable star universality

Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.Comment: 9 pages, 9 figures, accepted for publication in Physica

Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven Duffing oscillator

Different mechanisms for the creation of strange nonchaotic attractors (SNAs) are studied in a two-frequency parametrically driven Duffing oscillator. We focus on intermittency transitions in particular, and show that SNAs in this system are created through quasiperiodic saddle-node bifurcations (Type-I intermittency) as well as through a quasiperiodic subharmonic bifurcation (Type-III intermittency). The intermittent attractors are characterized via a number of Lyapunov measures including the behavior of the largest nontrivial Lyapunov exponent and its variance as well as through distributions of finite-time Lyapunov exponents. These attractors are ubiquitous in quasiperiodically driven systems; the regions of occurrence of various SNAs are identified in a phase diagram of the Duffing system.Comment: 24 pages, RevTeX 4, 12 EPS figure

On the importance of the convergence to climate attractors

Ensemble approaches are becoming widely used in climate research. In contrast to weather forecast, however, in the climatic context one is interested in long-time properties, those arising on the scale of several decades. The well-known strong internal variability of the climate system implies the existence of a related dynamical attractor with chaotic properties. Under the condition of climate change this should be a snapshot attractor, naturally arising in an ensemble-based framework. Although ensemble averages can be evaluated at any instant of time, results obtained during the process of convergence of the ensemble towards the attractor are not relevant from the point of view of climate. In simulations, therefore, attention should be paid to whether the convergence to the attractor has taken place. We point out that this convergence is of exponential character, therefore, in a finite amount of time after initialization relevant results can be obtained. The role of the time scale separation due to the presence of the deep ocean is discussed from the point of view of ensemble simulations