Regularity and stochasticity of nonlinear dynamical systems

Date

2017-06-01

Author

Akhmet, Marat

Metadata

Show full item record

Item Usage Stats

304
views

0
downloads

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

URI

https://hdl.handle.net/11511/86690

Relation

Grazing in impulsive differential equations

Collections

Department of Mathematics, Book / Book chapter

Suggestions

OpenMETU
Core

Functional Differential Equations with Piecewise Constant Argument Akhmet, Marat (null, 2017-06-01) This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing ...
Almost periodicity, chaos, and asymptotic equivalence Akhmet, Marat (Springer, 2019-06-01) The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets....
Sensor fusion, sensitivity analysis and calibration in shooter localization systems Akman, Caglar; Sonmez, Tolga; Ozugur, Ozgur; Basil, Abdil Burak; Leblebicioğlu, Mehmet Kemal (Elsevier BV, 2018-03-01) This paper analyses the principles and the underlying mathematical model for acoustic based shooter detection systems. These systems use the muzzle blast and acoustic shock waves to compute the shooter's location. Our detection system works on a distributed sensor network where microphone arrays are used as sensors. Detection algorithms run concurrently at each node. After determining the wave directions, the information is passed to the central node. The central node fuses data coming from each sensor with...
Hybrid wavelet-neural network models for time series data Kılıç, Deniz Kenan; Uğur, Ömür; Department of Financial Mathematics (2021-3-3) The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (∧GSPC) and NASDAQ (∧ IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. ...
Nonlinear estimation techniques applied to econometric problems Aslan, Serdar; Demirbaş, Kerim; Department of Electrical and Electronics Engineering (2004) This thesis considers the filtering and prediction problems of nonlinear noisy econometric systems. As a filter/predictor, the standard tool Extended Kalman Filter and new approaches Discrete Quantization Filter and Sequential Importance Resampling Filter are used. The algorithms are compared by using Monte Carlo Simulation technique. The advantages of the new algorithms over Extended Kalman Filter are shown.

Citation Formats

M. Akhmet, Regularity and stochasticity of nonlinear dynamical systems. 2017, p. 159.