Related papers: Poincare return maps in neural dynamics: three exa…

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…

A common approach for modeling the environment of an autonomous vehicle are dynamic occupancy grid maps, in which the surrounding is divided into cells, each containing the occupancy and velocity state of its location. Despite the advantage…

We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…

The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…

We show that, under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are topologically equivalent.

This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…

Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map…

One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…

Competition between synapses arises in some forms of correlation-based plasticity. Here we propose a game theory-inspired model of synaptic interactions whose dynamics is driven by competition between synapses in their weak and strong…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…

Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…