Related papers: A New Lorenz System Parameter Determination Method…
We present a new theoretical framework for designing linear parameter varying controllers in the polynomial chaos framework. We assume the scheduling variable to be random and apply polynomial chaos approach to synthesize the controller for…
We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and…
Changes in parameters of a physical device can eventually lead to catastrophic failure. This paper discusses a parameter estimation method based on synchronization between a model and time series data. In particular, we examine the…
This paper revisits the send/retrieve message process using synchronization of the Lorenz system with a monochromatic message. We analyze how the fidelity of the retrieved signal depends on the message frequency and demonstrate message…
In the paper, several concrete examples, as well as their numerical simulations, are given to show that parameter identification based on the so-called adaptive synchronization techniques might be failed if those functions with parameters…
The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The…
A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…
Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts,…
A discrete-time discrete-value pseudo-chaotic encoder/decoder system is presented. The pseudo-chaotic module is a 3D discrete version of the well-known Lorenz dynamical system. Scaling and biasing transformations as well as natural number…
Scientific analysis often relies on the ability to make accurate predictions of a system's dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model…
Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when such data is moreover highly corrupted, for example, due to the…
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed…
A new method based on the phenomenon of synchronization and the properties of chaos is proposed to reduce interference in the transferred chaotic signals of synchronized systems. In this paper, the interference is considered as a series of…
The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and…
Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically…
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…
Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…