Related papers: Topological-numerical analysis of a two-dimensiona…
This study investigates how dynamical systems may be learned and modelled with a neuromorphic network which is itself a dynamical system. The neuromorphic network used in this study is based on a complex electrical circuit comprised of…
This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme…
Emulate the gating mechanism of ionic channels in neurons, we present a mathematical model for the time constant of dynamical systems. Our model is an analytical continues function. The analyses give evidence that one can adjust the…
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
Neural systems can be modeled as networks of functionally connected neural elements. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…
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…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
Despite their importance for the spread of zoonotic diseases, our understanding of the dynamical aspects characterizing the movements of farmed animal populations remains limited as these systems are traditionally studied as static objects…
Learning topological representation of a network in dynamic environments has recently attracted considerable attention due to the time-evolving nature of many real-world networks i.e. nodes/links might be added/removed as time goes on.…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the…
In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
This paper addresses the problem of online network topology inference for expanding graphs from a stream of spatiotemporal signals. Online algorithms for dynamic graph learning are crucial in delay-sensitive applications or when changes in…
In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological…
Small disturbances can trigger functional breakdowns in complex systems. A challenging task is to infer the structural cause of a disturbance in a networked system, soon enough to prevent a catastrophe. We present a graph neural network…