The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sineGordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and e...

Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics. Originally phenomenon of chaos was associated with problems of classical mechanics and statistical physics. Attempt of substantiation of statistical mechanics initiated intensive study of chaos and uncover its basic properties main...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

purpose : to compare laser interferometry (li) and ultrasound a-scan in measurement of axial length ( al ) in eyes with asteroid hyalosis methods : twenty three patients with unilateral moderate to severe asteroid hyalosis determined by b-scan ultrasonography images participated in the study. the al measurements were obtained by li and ultrasound a-scan in both asteroid hyalosis and noninvolved...

– Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean field models. We consider a model spin glass on a tree and show that although it has mean field behavior with replica symmetry breaking, it manifestly has...

Noise-induced chaos is an interesting phenomenon. However, it is a subtle issue because of the difficulty in distinguishing between true low-dimensional chaos and noise. In this review article, we consider how to define noise-induced chaos and what constitutes a test for noise-induced chaos. The mechanism for noise-induced chaos is studied by considering the long-term growth rate of the logarit...

Chaotic home lives are correlated with behavior problems in children. In the study reported here, we tested whether there was a cross-lagged relation between children's experience of chaos and their disruptive behaviors (conduct problems and hyperactivity-inattention). Using genetically informative models, we then tested for the first time whether the influence of household chaos on disruptive ...