Related papers: Detecting chaos in a complex system
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
When a medium composed of microscopic elements is subjected to a high intensity field, the individual behaviors of microscopic elements can become chaotic. In such cases it is important to consider the effects of this irregularity at…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e.,…
The wave properties of complex scattering systems that are large compared to the wavelength, and show chaos in the classical limit, are extremely sensitive to system details. A solution to the wave equation for a specific configuration can…
Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we show how the partial control method can be applied in this kind of…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and R\"ossler models with their iconic attractors, and demonstrate…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
Quantum chaos is usually characterized through its statistical implications on the energy spectrum of a given system. In this work we propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system…
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
Complex networks obtained from the real-world networks are often characterized by incompleteness and noise, consequences of limited sampling as well as artifacts in the acquisition process. Because the characterization, analysis and…
The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the presentwork it is…
It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not…
The mechanism responsible for the emergence of chaotic behavior has been identified analytically within a class of three-dimensional dynamical systems which generalize the well-known E.N. Lorenz 1963 system. The dynamics in the phase space…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli…