Related papers: Chain Paradoxes
Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…
In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is…
Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
The main objective of this paper is to address the instability and dynamical bifurcation of the Dean problem. A nonlinear theory is obtained for the Dean problem, leading in particular to rigorous justifications of the linear theory used by…