Related papers: Lyapunov Exponent Evaluation of the CBC Mode of Op…
This paper describes the security weakness of a recently proposed secure communication method based on parameter modulation of a chaotic system and adaptive observer-based synchronization scheme. We show that the security is compromised…
In this paper, we discuss the asymptotic behavior of the Upper Confidence Bound (UCB) algorithm in the context of multiarmed bandit problems and discuss its implication in downstream inferential tasks. While inferential tasks become…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…
In dealing with nonlinear systems, it is common to use numerical solutions. Unlike the careful behavior towards the numerical results in chaotic regions, the validity of numerical results in regions of transient chaos might not always be…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart…
Safe navigation in unknown and cluttered environments remains a challenging problem in robotics. Model Predictive Contour Control (MPCC) has shown promise for performant obstacle avoidance by enabling precise and agile trajectory tracking,…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
The information security has an irreplaceable position in the smart grid (SG). In order to avoid the malicious attack and ensure the information security, the cryptographic techniques are essential. This paper focuses on the encryption…
We investigate the discretized version of the thermodynamic Bethe ansatz equation for a variety of 1+1 dimensional quantum field theories. By computing Lyapunov exponents we establish that many systems of this type exhibit chaotic…
We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier…
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…
We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter…
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 stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent…
With the ever increasing volume of information over wireless medium, security has assumed an important dimension. The security of transmitted data over a wireless channel aims at protecting the data from unauthorized intrusion. Wireless…
The component-by-component (CBC) algorithm is a method for constructing good generating vectors for lattice rules for the efficient computation of high-dimensional integrals in the "weighted" function space setting introduced by Sloan and…
Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for…
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors,…