Using Monotone Inputs to Solve Complex Network Dynamics

Summary

This work describes a method for determining the response of certain networks to arbitrary inputs by first characterizing their response to a monotone input. It applies to networks of any topology and allows nodes to have discrete or continuous states, without imposing a limit on network complexity. The result offers a route to efficient numerical computation and potentially accurate analytic approximations.

The authors illustrate the framework with a quasistatic mechanical system in which objects interact through friction, and with a financial market model where momentum trading generates avalanches and critical behavior. The excerpt does not provide specific equations, empirical data, or validation results for the financial model, so its relevance to trading should be read as a modeling application rather than evidence of a deployable strategy. The stated conclusions apply to the specified class of node dynamics.

Key ideas

• For a class of node dynamics, network response to arbitrary inputs can be derived from response to monotone inputs.
• The framework allows networks of any topology and nodes with discrete or continuous states.
• The method may support efficient numerical solutions and analytic approximations.
• Applications include frictional mechanical interactions and a market model with momentum-driven avalanches and critical behavior.
• The excerpt gives no empirical validation or trading performance results.

Tags

# Analytical solution for a class of network dynamics with mechanical and financial applications


# Analytical solution for a class of network dynamics with mechanical and financial applications









We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces, and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.