Brief Communication: Breeding vectors in the phase space reconstructed from time series data

Erin Lynch,Kayo Ide,Daniel Kaufman,Eugenia Kalnay,A Surjalal Sharma

doi:10.5194/npg-23-137-2016

Abstract

Abstract. Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

Highlights

Prediction of sudden regime changes in the evolution of dynamical systems is a challenging problem
The data-derived models of magnetospheric substorms and geospace storms (Vassiliadis et al, 1995; Ukhorskiy et al, 2002; Valdivia et al, 1996) provide near-real-time forecasts using the solar wind data monitored by the Advanced Composition Explorer (ACE) spacecraft at the first Lagrange point (L1)
This paper presents a novel extension of the original breeding technique to the phase space reconstructed from time series data using the time-delay embedding method

Summary

Introduction

Prediction of sudden regime changes in the evolution of dynamical systems is a challenging problem. Evans et al (2004) demonstrated that the growth rate of the bred vectors could be used as a means of predicting the regime changes in the chaotic Lorenz (1963) system (Lorenz, 1963). The variables or degrees of freedom are nonlinearly coupled, and in dissipative systems the dimensionality of the phase space is significantly reduced. This is the basis for the time-delay embedding method in the reconstruction of phase space (Packard et al, 1980; Takens, 1981). Reconstruction of the dynamics of the Earth’s magnetosphere using time series data has led to low-dimensional models and forecasts of space weather (Sharma et al, 1993; Sharma, 1995). The data-derived models of magnetospheric substorms and geospace storms (Vassiliadis et al, 1995; Ukhorskiy et al, 2002; Valdivia et al, 1996) provide near-real-time forecasts using the solar wind data monitored by the Advanced Composition Explorer (ACE) spacecraft at the first Lagrange point (L1)

Objectives

Results

Conclusion