Related papers: Advancing Chaos Theory: A Set-Valued Perspective o…
Machine learning processes, e.g. ''learning in games'', can be viewed as non-linear dynamical systems. In general, such systems exhibit a wide spectrum of behaviors, ranging from stability/recurrence to the undesirable phenomena of chaos…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
One propounded theory for the presence of chaos in biological neural networks is that it could be involved in discriminating different olfactory stimuli. Inspired by the idea, in this paper, we define the visual ``chaotic perception'' and…
We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We explore connections among the regional proximal relation, the asymptotic relation and the distal relation for a topological dynamical system with the shadowing property, and show that if a Devaney chaotic system has the shadowing…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
In this paper, we introduce a hybrid chaos map for image encryption method with high sensitivity. This new map is sensitive to small changes in the starting point and also in control parameters which result in having more computational…
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing. We demonstrate numerically that…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…
Existing methods for anomaly detection often fall short due to their inability to handle the complexity, heterogeneity, and high dimensionality inherent in real-world mobility data. In this paper, we propose DeepBayesic, a novel framework…
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…