Related papers: Exact expression for maximum Lyapunov exponent dur…
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…
In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide…
Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as…
Predicting extreme events in high-dimensional chaotic dynamical systems remains a fundamental challenge, as such events are rare, intermittent, and arise from transient dynamical mechanisms that are difficult to infer from limited…
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth neural ODEs. We demonstrate that FTLEs are powerful…
We study the dynamics of systems with different time scales, when access only to the slow variables is allowed. We use the concept of Finite Size Lyapunov Exponent (FSLE) and consider both the case when the equations of motion for the slow…
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…
In infrastructure-less highly dynamic networks, computing and performing even basic tasks (such as routing and broadcasting) is a very challenging activity due to the fact that connectivity does not necessarily hold, and the network may…
Traditional algorithms to optimize artificial neural networks when confronted with a supervised learning task are usually exploitation-type relaxational dynamics such as gradient descent (GD). Here, we explore the dynamics of the neural…
Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…
Recurrent Neural Networks (RNN) are ubiquitous computing systems for sequences and multivariate time series data. While several robust architectures of RNN are known, it is unclear how to relate RNN initialization, architecture, and other…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
Complex-valued bidirectional associative memory (BAM) neural networks with fractional-order dynamics and delays can exhibit transient instabilities that degrade synchronization and short-horizon predictability. This paper develops a unified…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
We study the transients of linear max-plus dynamical systems. For that, we consider for each irreducible max-plus matrix A, the weighted graph G(A) such that A is the adjacency matrix of G(A). Based on a novel graph-theoretic counterpart to…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
Identifying phase transitions and classifying phases of matter is central to understanding the properties and behavior of a broad range of material systems. In recent years, machine-learning (ML) techniques have been successfully applied to…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…