Related papers: Chaos, concentration, and multiple valleys
The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…
Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical…
The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry,…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
Cells can often choose among several stably heritable phenotypes. Examples are the expression of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states, that may be associated…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
Systems with a complex dynamics like glasses or models of biological evolution are often pictured in terms of complex landscapes, with a large number of possible collective states. We show on the example of a stochastic spin model with…
It has recently been shown that one-dimensional Ising problems can have degenerate, disordered ground states (GSs) over a finite range of coupling onstants, ie, without `fine tuning'. The disorder is however of a special kind, consisting of…
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…
The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots…
A new numerical method to calculate exact ground states of multi-fluxline systems with quenched disorder is presented, which is based on the minimum cost flow algorithm from combinatorial optimization. We discuss several models that can be…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is $\lambda \ll \ell$, where $\lambda$ is the…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…