Detection of chaotic behavior in time series

Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and statistical properties as well as to infer short time-series. Our successful modeling relies on the introduction of a set of Gaussian radial basis functions to capture local structure. The proposed method is used to construct a system of ordinary differential equations whose orbit reconstructs a time-series of a variable of the well-known Lorenz system as a simp…

Classification of chaotic time series with deep learning

We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some of the most challenging real-life applications is to train different neural networks on a data set from a dynamical system with a basic or low-dimensional phase space and then use these networks to classify univariate time series of a dynamical system with more intricate or high-dimensional phase space. We illustrate this generalisation approach using the log…

一种用于混沌时间序列预测的张量网络方法

A tensor network approach for chaotic time series prediction

针对混沌时间序列预测问题，提出基于张量网络的模型，通过分解高维数组降低参数复杂度，在精度和计算效率上优于传统回声状态网络。

Model-free prediction of noisy chaotic time series by deep learning

We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long Short-Term Memory network (LSTM) is employed to model the nonlinear dynamics and a softmax layer is used to approximate a probability distribution. The LSTM model is trained by minimizing a regularized cross-entropy function. The LSTM model is validated against delay-time chaotic dynamical systems, Mackey-Glass and Ikeda equations. It is shown that the present L…

Chaotic Behavior of Positronium in a Magnetic Field

Classical motion of positronium embedded in a magnetic field is studied, and computation shows the emergence of chaotic orbits. Recent work investigating quantum behavior of this system predicts extremely long lifetimes. Chaos assisted tunneling, however may lead to significant shortening of the lifetime of this system.

Bistable non-volatile elastic membrane memcapacitor exhibiting chaotic behavior

We suggest a realization of a bistable non-volatile memory capacitor (memcapacitor). Its design utilizes a strained elastic membrane as a plate of a parallel-plate capacitor. The applied stress generates low and high capacitance configurations of the system. We demonstrate that a voltage pulse of an appropriate amplitude can be used to reliably switch the memcapacitor into the desired capacitance state. Moreover, charged-voltage and capacitance-voltage curves of such a system demonstrate hysteresis and transition into a chaotic regime in a certain range of ac voltage amplitudes and frequencies…