Results 1 - 10 of 2159
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[en] Iterated function systems which consist of discontinuous maps are shown to be able to have attractors in the sense of Hutchinson. Moreover, it is demonstrated that discontinuous systems often admit strict attractors which are non-invariant, so one can call them homoclinic attractors. The existence of such attractors relates to the notion of a fast basin.
[en] A map of a space into itself generates weighted shift operators in function spaces on . The spectral properties of such operators are intimately connected with the dynamics of . It was known previously that the spectrum of an operator depends only on the set of invariant ergodic measures for . Conditions for the right invertibility of the operators are obtained when is a spectral value. The main result states that right invertibility is only possible when a nontrivial attractor exists. Bibliography: 29 titles.
[en] We investigate the evolution of cosmological perturbations in scenarios with a quintessence scalar field, both analytically and numerically. In the tracking regime for quintessence, we find the long wavelength solutions for the perturbations of the quintessence field. We discuss the possibility of isocurvature modes generated by the quintessence sector
[en] Our aim in this paper is to study the well-posedness and the dissipativity of higher-order anisotropic conservative phase-field systems. More precisely, we prove the existence and uniqueness of solutions and the existence of the global attractor.
[en] A generalization is considered of Williams's well-known model of the attractor in the Lorenz system, the inverse limit of semiflows on branched manifolds that are suspensions over a discontinuous expanding map of a closed line interval. The generalization consists in the consideration of maps with several, rather than one, discontinuity points. A cardinal-valued topological invariant L-manuscript is constructed, which distinguishes a continuum of non-homeomorphic generalized models. A topological invariant distinguishing a continuum of non-homeomorphic geometric Lorenz attractors is obtained as a consequence.
[en] We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo–Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of parameter values
[en] In this article, we consider a system of autonomous inductively coupled Van der Pol generators. For two coupled generators, we establish the presence of metastable chaos, a strange non-chaotic attractor, and several stable limiting cycles. Areas of parametric dependence of different modes of synchronization are obtained
[en] Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, which contains three different chaotic attractors, i.e., the conjugate Lorenz attractor, the conjugate Chen attractor and the conjugate Lue attractor. These new attractors are conjugate, respectively, to the Lorenz attractor, the Chen attractor and the Lue attractor in an algebraic sense. The conjugate attractors may be helpful for finally revealing the geometric structure of the Lorenz attractor.
[en] We show a type of unpredictability of the Wada property in the parameter plane for fixed initial conditions. This property indicates a larger unpredictability of sensitive dependence on parameters except for the riddled parameter sets. We describe some numerical experiments giving evidences of the parameter Wada property for different types of attractors including strange nonchaotic attractors. A scaling exponent is used to characterize sensitive dependence on parameters. We present a qualitative explanation on the occurrence of the Wada property in the parameter plane. -- Highlights: ► We report the Wada property of the parameter subsets for several types of attractors (periodic attractors, quasiperiodic attractors, strange nonchaotic attractors, etc.). ► The mechanisms of the Wada property in the parameter plane were examined. ► This property of the parameter subsets indicates a larger unpredictability of alternative stable states.