Related papers: Analyzing Topological Mixing and Chaos on Continua…
It is shown that in a topological dynamical system with positive entropy, there is a measure-theoretically "rather big" set such that a multivariant version of mean Li-Yorke chaos happens on the closure of the stable or unstable set of any…
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…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We prove that if a topological dynamical system is mean sensitive and contains a mean proximal pair consisting of a transitive point and a periodic point, then it is mean Li-Yorke chaotic (DC2 chaotic). On the other hand we show that a…
In this work we consider two models of two dimensional discrete systems subjected to three different types of coupling and analyse systematically the performance of each in realising synchronised states.We find that linear coupling…
In recent years, the generation of rigorously provable chaos in finite precision digital domain has made a lot of progress in theory and practice, this article is a part of it. It aims to improve and expand the theoretical and application…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Topological effects produce chaos in multiagent simulation and distributed computation. We explain this result by developing three themes concerning complex systems in the natural and social sciences: (i) Pragmatically, a system is complex…
In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time…
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…
We investigate several dynamical regimes characterizing a bosonic binary mixture loaded in a ring trimer, with particular reference to the persistence of demixing. The degree of phase separation is evaluated by means of the "Entropy of…
This talk summarises what is currently understood about the phenomenon that has come to be known as {\it chaotic mixing}. The first part presents a concise statement as to what chaotic mixing actually is, and then explains why it should be…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving 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…