Asynchronous Networks and Event Driven Dynamics

Abstract

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks.

References in corpus (7)

• Analysis of a power grid using the Kuramoto-like model
• Comparative analysis of existing models for power-grid synchronization
• Dynamical Systems on Networks: A Tutorial
• Chimera states in two populations with heterogeneous phase-lag
• Chaos synchronization in networks of coupled maps with time-varying topologies
• Asynchronous Networks: Modularization of Dynamics Theorem
• Graph fibrations and symmetries of network dynamics

Cited by in corpus (10)

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• Asynchronous Networks: Modularization of Dynamics Theorem
• Symmetry & critical points for a model shallow neural network
• Amplified steady state bifurcations in feedforward networks
• Nesting of dynamic systems and mode-dependent networks
• Homogeneous coupled cell systems with high-dimensional internal dynamics
• Diffusion in Networks and the Unexpected Virtue of Burstiness