相关论文: A closed form for Jacobian reconstruction from tim…
In this paper, a hybrid measurement and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network topology.…
In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network…
In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix and the dynamic system state matrix in near real-time utilizing statistical properties extracted from PMU…
Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no…
The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…
Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…
Key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures.…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
Quantifying interaction strengths between state variables in dynamical systems is essential for understanding ecological networks. Within the empirical dynamic modeling approach, multivariate S-map infers the interaction Jacobian from time…
The image-based visual servoing without models of system is challenging since it is hard to fetch an accurate estimation of hand-eye relationship via merely visual measurement. Whereas, the accuracy of estimated hand-eye relationship…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…
Ecological systems are studied using many different approaches and mathematical tools. One approach, based on the Jacobian of Lotka-Volterra type models, has been a staple of mathematical ecology for years, leading to many ideas such as on…
Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…
Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be…