Results 61 to 70 of about 3,260 (185)

Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems

Algorithms, 2017
Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge–Kutta problems that need to be calculated.
Jorge J. Hernández-Gómez, Carlos Couder-Castañeda, Israel E. Herrera-Díaz, Norberto Flores-Guzmán, Enrique Gómez-Cruz   +4 more
doaj   +1 more source

Neural‐Network‐Based Event‐Triggered Consensus Tracking for Nonlinear Heterogeneous Multi‐Agent Systems Against Denial‐of‐Service Attacks

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This article proposes a distributed resilient control framework to ensure consensus tracking for nonlinear heterogeneous multi‐agent systems (NHMAS) under aperiodic denial‐of‐service (DoS) attacks. First, a resilient observer is introduced to estimate the leader's state considering that not all agents have direct access to the leader's ...
Li Liu, Bing Yan, Junkang Ni, Peng Shi
wiley   +1 more source

On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative

Journal of Mathematics, 2020
In this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the ...
Ndolane Sene, Ameth Ndiaye
doaj   +1 more source

On Lyapunov exponents and adversarial perturbation

CoRR, 2018
In this paper, we would like to disseminate a serendipitous discovery involving Lyapunov exponents of a 1-D time series and their use in serving as a filtering defense tool against a specific kind of deep adversarial perturbation. To this end, we use the state-of-the-art CleverHans library to generate adversarial perturbations against a standard ...
Vinay Uday Prabhu, Nishant Desai, John Whaley   +2 more
openaire   +2 more sources

Removing zero Lyapunov exponents [PDF]

Ergodic Theory and Dynamical Systems, 2003
Motivated by \textit{M. Shub} and \textit{A. Wilkinson}'s result [Invent. Math. 139, 495--508 (2000; Zbl 0976.37013)] for an explicit family of partially hyperbolic diffeomorphisms of the torus \(T^3\) in perturbing the Lyapunov exponents of the center direction, the authors present a local version of their arguments, allowing one to perturb the center
Baraviera, Alexandre T., Bonatti, Christian   +1 more
openaire   +2 more sources

Anchor Flow Maps: Efficient Sampling and Approximation of the Entire Flow Map

Computer Graphics Forum, EarlyView.
Abstract Flow maps are a fundamental concept for the visualization and analysis of time‐dependent flows. A common approach is to apply sampling and reconstruction – which comes with a number of problems: flow maps are high‐dimensional functions with locally large gradients which makes approximations very challenging.
D. Stelter, T. Wilde, C. Rössl, H. Theisel   +3 more
wiley   +1 more source

Lyapunov analysis of data-driven models of high dimensional dynamics using reservoir computing: Lorenz-96 system and fluid flow

Journal of Physics: Complexity
We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a highly dimensionally unstable structure.
Miki U Kobayashi, Kengo Nakai, Yoshitaka Saiki   +2 more
doaj   +1 more source

Lyapunov exponents, phase transition and chaos bound in Kerr-Newman AdS spacetime

Nuclear Physics B
In this paper, we investigate Lyapunov exponents associated with chaotic motions of both massless and massive particles in the vicinity of a Kerr-Newman AdS black hole.
Chuang Yang, Chuanhong Gao, Deyou Chen, Xiaoxiong Zeng   +3 more
doaj   +1 more source

Lyapunov Exponents and Sensitive Dependence

Journal of Dynamics and Differential Equations, 2010
Precise relationships between Lyapunov exponents and the instability/stability of orbits of scalar discrete dynamical systems are investigated. It is known that positive Lyapunov exponent does not, in general, imply instability, or, equivalently, sensitive dependence on initial conditions.
Kocak, Hueseyin, Palmer, Kenneth J.
openaire   +2 more sources

Parametric Time‐Variation in the Unconditional Volatility: Estimation and Inference

Journal of Time Series Analysis, EarlyView.
ABSTRACT We propose modeling time‐variation in the unconditional volatility by augmenting the standard GARCH model by a deterministic time‐varying intercept. The model, called the additive time‐varying (ATV‐)GARCH model, can be interpreted as a reduced form of a model including covariates and can be derived from a multiplicative decomposition of ...
Niklas Ahlgren, Alexander Back, Timo Teräsvirta   +2 more
wiley   +1 more source