Related papers: Automatic recognition and tagging of topologically…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…

Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the…

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are…

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…

In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions…

Given an unknown dynamic system such as a coupled harmonic oscillator with $n$ springs and point masses. We are often interested in gaining insights into its physical parameters, i.e. stiffnesses and masses, by observing trajectories of…

Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…

Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a…

The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…