scholarly journals Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yvonne Krumbeck ◽  
Qian Yang ◽  
George W. A. Constable ◽  
Tim Rogers
Keyword(s):  
Dynamical Systems ◽  
Time Series Data ◽  
Matrix Theory ◽  
Equilibrium Points ◽  
Temporal Stability ◽  
Ecological Networks ◽  
Series Data ◽  
Extrinsic Noise ◽  
Open Question ◽  
Important Notion

AbstractUnderstanding the relationship between complexity and stability in large dynamical systems—such as ecosystems—remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of ‘stability’ in fact has other uses in the empirical ecological literature. The important notion of ‘temporal stability’ describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis of ecological time-series data of plankton abundances.

scholarly journals Informing management decisions for ecological networks, using dynamic models calibrated to noisy time‐series data

2020 ◽  
Vol 23 (4) ◽  
pp. 607-619 ◽  
Author(s):  
Matthew P. Adams ◽  
Scott A. Sisson ◽  
Kate J. Helmstedt ◽  
Christopher M. Baker ◽  
Matthew H. Holden ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamic Models ◽  
Time Series Data ◽  
Ecological Networks ◽  
Series Data ◽  
Management Decisions ◽  
Noisy Time Series

scholarly journals Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

2020 ◽  
Author(s):  
Robert Glenn Moulder ◽  
Elena Martynova ◽  
Steven M. Boker
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Series Data ◽  
Alternative View ◽  
Unified Framework ◽  
Nonlinear Dynamical ◽  
Depth Analysis ◽  
Analysis Of Time Series

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies.

scholarly journals Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks

2021 ◽  
Author(s):  
Sibo Cheng ◽  
Mingming Qiu
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Series Data ◽  
Observation Data ◽  
Observation Error ◽  
Error Covariance

AbstractData assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

scholarly journals Reconstructing ecological networks with noisy dynamics

2020 ◽  
Vol 476 (2237) ◽  
pp. 20190739 ◽  
Author(s):  
Mara A. Freilich ◽  
Rolando Rebolledo ◽  
Derek Corcoran ◽  
Pablo A. Marquet
Keyword(s):  
Time Series ◽  
Network Topology ◽  
Network Structure ◽  
Time Series Data ◽  
Species Abundance ◽  
Intrinsic Noise ◽  
Ecological Networks ◽  
Series Data ◽  
Statistical Techniques ◽  
Time Series Data Analysis

Ecosystems functioning is based on an intricate web of interactions among living entities. Most of these interactions are difficult to observe, especially when the diversity of interacting entities is large and they are of small size and abundance. To sidestep this limitation, it has become common to infer the network structure of ecosystems from time series of species abundance, but it is not clear how well can networks be reconstructed, especially in the presence of stochasticity that propagates through ecological networks. We evaluate the effects of intrinsic noise and network topology on the performance of different methods of inferring network structure from time-series data. Analysis of seven different four-species motifs using a stochastic model demonstrates that star-shaped motifs are differentially detected by these methods while rings are differentially constructed. The ability to reconstruct the network is unaffected by the magnitude of stochasticity in the population dynamics. Instead, interaction between the stochastic and deterministic parts of the system determines the path that the whole system takes to equilibrium and shapes the species covariance. We highlight the effects of long transients on the path to equilibrium and suggest a path forward for developing more ecologically sound statistical techniques.

scholarly journals Methods for the Evaluation of the Stochastic Properties of the Ionosphere for Earthquake Prediction—Random Matrix Theory

Atmosphere ◽  
2019 ◽  
Vol 10 (7) ◽  
pp. 413 ◽  
Author(s):  
Leontýna Břizová ◽  
Jan Kříž ◽  
Filip Studnička ◽  
Jan Šlégr
Keyword(s):  
Earthquake Prediction ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Time Series Data ◽  
Matrix Theory ◽  
Low Frequency ◽  
Lower Ionosphere ◽  
Causal Chain ◽  
Series Data ◽  
Stochastic Properties

Seismo-ionospheric coupling is a field of great interest and is currently subject to rigorous study; using both ground and satellite data and many phenomenological features, the ionospheric precursors of earthquakes were identified. In this work, we present methods to study the stochastic properties of the lower ionosphere, derived from the data obtained with very low frequency (VLF) receivers at frequencies in the range of 19.6 to 37.5 kHz. Two main approaches are described: auto-correlation and random matrix theory treatments of amplitude time series data. It is shown that before shallow earthquakes with magnitudes greater than four, there are measurable changes that can be used in earthquake prediction. Although the exact form of the causal chain that leads to these changes are currently subject to diligent study, we believe that the investigations described herein are worth adding to the repertoire of ionospheric precursors.

scholarly journals Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Vandana Sakhre ◽  
Sanjeev Jain ◽  
Vilas S. Sapkal ◽  
Dev P. Agarwal
Keyword(s):  
Neural Network ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Back Propagation ◽  
Network Control ◽  
Series Data ◽  
Nonlinear Dynamical ◽  
Single Output ◽  
Propagation Network

Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data.

Data-Mining Dynamical Systems: Automated Symbolic System Identification for Exploratory Analysis

2008 ◽  
Author(s):  
Michael D. Schmidt ◽  
Hod Lipson
Keyword(s):  
System Identification ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Exploratory Analysis ◽  
Analytical Models ◽  
Series Data ◽  
Symbolic System ◽  
The Core ◽  
Nonlinear Mechanical ◽  
Programming Techniques

This paper describes a new algorithm for automatically reverse-engineering symbolic analytical models of dynamical systems directly from experimental observations, for the purpose of modeling, control and exploratory analysis. The new algorithm builds on genetic programming techniques used in symbolic regression to infer differential equations from time series data. We introduce the core algorithm for building coherent mathematical models efficiently and then describe its application to system identification. The method is demonstrated on a number of nonlinear mechanical and biological systems.

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