Z. Naturforsch. 48 a, 679-691 (1993); received February 17, 1993 This paper is dedicated to the memory of our friends and colleagues Christoph K. Goertz, Dwight R. Nicholson, Linhua Shan, and Robert A. Smith, who were tragically slain on November 1, 1991 A new base for three-dimensional divergence-free vector fields in Hilbert space (Galerkin method) is proposed. The base fields have vanishing ...

Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a non-compact but separable state space. Namely, the state space can be decomposed into a chain recurrent part and a gradient-like part. This result applies to ...

Similar looking Lorenz Curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz Curve and the modality of its underlying income density: Given a parametric Lorenz Curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e. do...

Abstract: This paper shows that a large class of chaotic systems, introduced in (Čelikovský and Vaněček, 1994), (Vaněček and Čelikovský, 1996) as the generalized Lorenz system, can be further generalized to the hyperbolic-type generalized Lorenz system. While the generalized Lorenz system unifies both the famous Lorenz system and new Chen’s system (Ueta and Chen, 1999), (Chen and Ueta, 2000), t...

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve L by a function h, giving rise to a distorted Lorenz curve (DLC) e L = h L. In this paper, we study, in an uni…ed framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aab...

We introduce a family of stochastic models motivated by the study nonequilibrium steady states fluid equations. These decompose deterministic dynamics interest into fundamental building blocks, i.e., minimal vector fields preserving some aspects original dynamics. Randomness is injected sequentially following each field for random amount time. show under general assumptions that these possess u...

We propose a comprehensive framework able to address both the predictability of first and second kind for high-dimensional chaotic models. For this purpose, we analyse properties newly introduced multistable climate toy model constructed by coupling Lorenz '96 with zero-dimensional energy balance model. First, attractors system are identified Monte Carlo Basin Bifurcation Analysis. Additionally...

Probability density P (x) is defined so that the probability to find a random variable x in the interval from x to x+ dx is equal to P (x) dx. Cumulative probability C(x) is defined as the integral C(x) = ∫∞ x P (x) dx. It gives the probability that the random variable exceeds a given value x. The Boltzmann-Gibbs distribution gives the probability of finding a physical system in a state with th...

Probability density P (x) is defined so that the probability to find a random variable x in the interval from x to x+ dx is equal to P (x) dx. Cumulative probability C(x) is defined as the integral C(x) = ∫∞ x P (x) dx. It gives the probability that the random variable exceeds a given value x. The Boltzmann-Gibbs distribution gives the probability of finding a physical system in a state with th...

Models occupy a central role in the scientific endeavour. Among the many purposes they serve, representation is of great importance. Many models are representations of something else; they stand for, depict, or imitate a selected part of the external world (often referred to as target system, parent system, original, or prototype). Well-known examples include the model of the solar system, the ...