Related papers: Designing Chaotic Attractors: A Semi-supervised Ap…
Reservoir computing can embed attractors into random neural networks (RNNs), generating a ``mirror'' of a target attractor because of its inherent symmetrical constraints. In these RNNs, we report that an attractor-merging crisis…
The dynamics of the tubular chemical reactor with mass recycle were examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper it has…
We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Our work presents a study on the nonlinear dynamical behavior for a microcavity semiconductor containing a quantum well. Using an external periodic perturbation in energy level we observe the periodic-doubling, quasiperiodic, and direct…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
Whereas the power of reservoir computing (RC) in inferring chaotic systems has been well established in the literature, the studies are mostly restricted to mono-functional machines where the training and testing data are acquired from the…
A new method of symbolic analysis based on finite discretization of velocity-curvature space is proposed. A minimum alphabet is introduced in a natural way, and a number of initial analytic measures are defined that make it possible to…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different,…
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth…
Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…