Related papers: Ergodic Sensitivity Analysis of One-Dimensional Ch…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Understanding brain dynamics in epilepsy is critical for establishing rigorous control objectives that enable new therapeutic methods to mitigate seizure occurrence. In multichannel electrocorticography (ECoG) recordings acquired in 21…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
We conduct a comprehensive investigation into the dynamics of gradient descent using large-order constant step-sizes in the context of quadratic regression models. Within this framework, we reveal that the dynamics can be encapsulated by a…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…
Chaotic logic gates or `chaogates' are a promising mixed-signal approach to designing universal computers. However, chaotic systems are exponentially sensitive to small perturbations, and the effects of noise can cause chaotic computers to…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
The Swift-Hohenberg fluid convection system with both local and nonlocal nonlinearities under the influence of white noise is studied. The objective is to understand the difference in the dynamical behavior in both local and nonlocal cases.…
We present a decentralized ergodic control policy for time-varying area coverage problems for multiple agents with nonlinear dynamics. Ergodic control allows us to specify distributions as objectives for area coverage problems for nonlinear…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from…
Forecasting the dynamics of chaotic systems from the analysis of their output signals is a challenging problem with applications in most fields of modern science. In this work, we use a laser model to compare the performance of several…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula…
The Hierarchy Of Time-Surfaces (HOTS) algorithm, a neuromorphic approach for feature extraction from event data, presents promising capabilities but faces challenges in accuracy and compatibility with neuromorphic hardware. In this paper,…
This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…