Chaotic Systems and Their Recent Implementations on Improving Intelligent Systems

2014 ◽  
pp. 69-101 ◽  
Author(s):  
Utku Köse ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Research Effort ◽  
Nonlinear Dynamical ◽  
Main Research ◽  
Reference Guide

Chaos Theory is a kind of a scientific approach/research effort which is based on examining behaviors of nonlinear dynamical systems which are highly sensitive to their initial conditions. Currently, there are many different scientific studies based on the Chaos Theory and the related solution approaches, methods, or techniques for problems of this theory. Additionally, the theory is used for improving the introduced studies of different fields in order to get more effective, efficient, and accurate results. At this point, this chapter aims to provide a review-based study introducing recent implementations of the Chaos Theory on improving intelligent systems, which can be examined in the context of the Artificial Intelligence field. In this sense, the main research way is directed into the works performed or introduced mostly in years between 2008 and 2013. By providing a review-based study, the readers are enabled to have ideas on Chaos Theory, Artificial Intelligence, and the related works that can be examined within intersection of both fields. At this point, the chapter aims to discuss not only recent works, but also express ideas regarding future directions within the related implementations of chaotic systems to improve intelligent systems. The chapter is generally organized as a reference guide for academics, researchers, and scientists tracking the literature of the related fields: Artificial Intelligence and the Chaos Theory.

scholarly journals Chaotic Systems and Their Recent Implementations on Improving Intelligent Systems

Economics ◽  
2015 ◽  
pp. 1167-1200
Author(s):  
Utku Köse ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Research Effort ◽  
Nonlinear Dynamical ◽  
Main Research ◽  
Reference Guide

Chaos Theory is a kind of a scientific approach/research effort which is based on examining behaviors of nonlinear dynamical systems which are highly sensitive to their initial conditions. Currently, there are many different scientific studies based on the Chaos Theory and the related solution approaches, methods, or techniques for problems of this theory. Additionally, the theory is used for improving the introduced studies of different fields in order to get more effective, efficient, and accurate results. At this point, this chapter aims to provide a review-based study introducing recent implementations of the Chaos Theory on improving intelligent systems, which can be examined in the context of the Artificial Intelligence field. In this sense, the main research way is directed into the works performed or introduced mostly in years between 2008 and 2013. By providing a review-based study, the readers are enabled to have ideas on Chaos Theory, Artificial Intelligence, and the related works that can be examined within intersection of both fields. At this point, the chapter aims to discuss not only recent works, but also express ideas regarding future directions within the related implementations of chaotic systems to improve intelligent systems. The chapter is generally organized as a reference guide for academics, researchers, and scientists tracking the literature of the related fields: Artificial Intelligence and the Chaos Theory.

A Web-Based Intelligent Educational Laboratory System for Forecasting Chaotic Time Series

2015 ◽  
pp. 110-135
Author(s):  
Utku Kose ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Time Series ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Chaotic Time Series ◽  
Laboratory System ◽  
Web Based ◽  
Intelligent Water Drops Algorithm ◽  
Forecast Time

In the context of Chaos Theory and its applications, forecasting time series of a chaotic system is an attractive work area for the current literature. Many different approaches and the related scientific studies have been introduced and done by researchers since the inception of this working area. Newer studies are also performed in order to provide more effective and efficient approaches and improve the related literature in this way. On the other hand, it is another important research point to ensure effective educational approaches for teaching Chaos Theory and chaotic systems within the associated courses. In this sense, this chapter introduces a Web-based, intelligent, educational laboratory system for forecasting chaotic time series. Briefly, the system aims to enable students to experience their own learning process over the Web by using a simple interface. The laboratory system employs an Artificial Intelligence-based approach including a Single Multiplicative Neuron System trained by Intelligent Water Drops Algorithm in order to forecast time series of chaotic systems. It is possible to adjust parameters of the related Artificial Intelligence techniques, so it may possible for students to have some knowledge about Artificial Intelligence and intelligent systems.

ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (03) ◽  
pp. 455-471 ◽  
Author(s):  
CHAI WAH WU ◽  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Adaptive Synchronization ◽  
Adaptive Controllers ◽  
Nonlinear Dynamical ◽  
Two Systems ◽  
And Control

In this paper, we study the synchronization of two coupled nonlinear, in particular chaotic, systems which are not identical. We show how adaptive controllers can be used to adjust the parameters of the systems such that the two systems will synchronize. We use a Lyapunov function approach to prove a global result which shows that our choice of controllers will synchronize the two systems. We show how it is related to Huberman-Lumer adaptive control and the LMS adaptive algorithm. We illustrate the applicability of this method using Chua's oscillators as the chaotic systems. We choose parameters for the two systems which are orders of magnitude apart to illustrate the effectiveness of the adaptive controllers. Finally, we discuss the role of adaptive synchronization in the context of secure and spread spectrum communication systems. In particular, we show how several signals can be encoded onto a single scalar chaotic carrier signal.

scholarly journals Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

2017 ◽  
Author(s):  
Geoff Boeing
Keyword(s):  
Dynamical Systems ◽  
Visual Analysis ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Systems Of Nonlinear Equations ◽  
Self Similarity ◽  
Nonlinear Dynamical ◽  
Qualitative Approaches ◽  
Divergent Behavior ◽  
Behavior Systems

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

scholarly journals iLQR-VAE : control-based learning of input-driven dynamics with applications to neural data

2021 ◽  
Author(s):  
Marine Schimel ◽  
Ta-Chu Kao ◽  
Kristopher T. Jensen ◽  
Guillaume Hennequin
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Linear Quadratic Regulator ◽  
External Input ◽  
Learning Approaches ◽  
Linear Quadratic ◽  
Nonlinear Dynamical ◽  
Neural Data ◽  
Recognition Model ◽  
Variational Autoencoder

Understanding how neural dynamics give rise to behaviour is one of the most fundamental questions in systems neuroscience. To achieve this, a common approach is to record neural populations in behaving animals, and model these data as emanating from a latent dynamical system whose state trajectories can then be related back to behavioural observations via some form of decoding. As recordings are typically performed in localized circuits that form only a part of the wider implicated network, it is important to simultaneously learn the local dynamics and infer any unobserved external input that might drive them. Here, we introduce iLQR-VAE, a novel control-based approach to variational inference in nonlinear dynamical systems, capable of learning both latent dynamics, initial conditions, and ongoing external inputs. As in recent deep learning approaches, our method is based on an input-driven sequential variational autoencoder (VAE). The main novelty lies in the use of the powerful iterative linear quadratic regulator algorithm (iLQR) in the recognition model. Optimization of the standard evidence lower-bound requires differentiating through iLQR solutions, which is made possible by recent advances in differentiable control. Importantly, having the recognition model implicitly defined by the generative model greatly reduces the number of free parameters and allows for flexible, high-quality inference. This makes it possible for instance to evaluate the model on a single long trial after training on smaller chunks. We demonstrate the effectiveness of iLQR-VAE on a range of synthetic systems, with autonomous as well as input-driven dynamics. We further show state-of-the-art performance on neural and behavioural recordings in non-human primates during two different reaching tasks.

COMPETITIVE MODES AND THEIR APPLICATION

2006 ◽  
Vol 16 (03) ◽  
pp. 497-522 ◽  
Author(s):  
WEIGUANG YAO ◽  
PEI YU ◽  
CHRISTOPHER ESSEX ◽  
MATT DAVISON
Keyword(s):  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Point Of View ◽  
Frequency Function ◽  
Mode Competition ◽  
Integration Scheme ◽  
Nonlinear Dynamical ◽  
Competitive Modes ◽  
Definition Of

We investigate nonlinear dynamical systems from the mode competition point of view, and propose the necessary conditions for a system to be chaotic. We conjecture that a chaotic system has at least two competitive modes (CM's). For a general nonlinear dynamical system, we give a simple, dynamically motivated definition of mode suitable for this concept. Since for most chaotic systems it is difficult to obtain the form of a CM, we focus on the competition between the corresponding modulated frequency components of the CM's. Some direct applications result from the explicit form of the frequency functions. One application is to estimate parameter regimes which may lead to chaos. It is shown that chaos may be found by analyzing the frequency function of the CM's without applying a numerical integration scheme. Another application is to create new chaotic systems using custom-designed CM's. Several new chaotic systems are reported.

scholarly journals Identification of nonlinear dynamical systems with time delay

2021 ◽  
Author(s):  
Ghazaale Leylaz ◽  
Shuo Wang ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Duffing Oscillator ◽  
Algebraic Operation ◽  
Computationally Efficient ◽  
Nonlinear Dynamical ◽  
Automatic Model Selection ◽  
Robust To Noise

AbstractThis paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended to nonlinear systems with time delay. The proposed algorithm combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

scholarly journals Artificial Intelligence, Chaos, Prediction and Understanding in Science

2021 ◽  
Vol 31 (11) ◽  
pp. 2150173
Author(s):  
Miguel A. F. Sanjuán
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Big Data ◽  
Deep Learning ◽  
Dynamical Systems ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Constructive Dialogue ◽  
Learning Techniques

Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main thesis here is that prediction and understanding are two very different and important ideas that should guide us to follow the progress of science. Furthermore, the important role played by nonlinear dynamical systems is emphasized for the process of understanding. The path of the future of science will be marked by a constructive dialogue between big data and big theory, without which we cannot understand.

Nonlinear Dynamical Systems, Their Stability, and Chaos

2014 ◽  
Vol 66 (2) ◽  
Author(s):  
Amol Marathe ◽  
Rama Govindarajan
Keyword(s):  
Fluid Flow ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Fluid Mechanics ◽  
Fixed Points ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Not Given ◽  
Nonlinear Dynamical ◽  
Detailed Explanation

This introduction to nonlinear systems is written for students of fluid mechanics, so connections are made throughout the text to familiar fluid flow systems. The aim is to present how nonlinear systems are qualitatively different from linear and to outline some simple procedures by which an understanding of nonlinear systems may be attempted. Considerable attention is paid to linear systems in the vicinity of fixed points, and it is discussed why this is relevant for nonlinear systems. A detailed explanation of chaos is not given, but a flavor of chaotic systems is presented. The focus is on physical understanding and not on mathematical rigor.

Sign in / Sign up

Export Citation Format

Share Document