Inferring bifurcation diagrams of two distinct chaotic systems by a single machine

TL;DR

This paper introduces a dual-channel reservoir computing approach that can infer and reconstruct bifurcation diagrams of two different chaotic systems using a single machine trained on limited data.

Contribution

The novel scheme enables simultaneous modeling of two chaotic systems with a single reservoir, incorporating system-label and parameter-control channels for improved inference.

Findings

Successfully predicts short-term dynamics of both systems.

Reproduces long-term statistical properties and bifurcation diagrams.

Distinguishes systems via distinct dynamical patterns in the reservoir.

Abstract

We propose a dual-channel reservoir-computing scheme for inferring the dynamics of two distinct chaotic systems with a single machine. By augmenting a standard reservoir with a system-label channel and a parameter-control channel, the machine can be trained from time series collected from a few sampled states of the two systems. We show that the trained machine not only predicts the short-time evolution of the sampled states, but also reproduces the long-term statistical properties of unseen states, thereby enabling reconstruction of the bifurcation diagrams of both systems from partial observations. The effectiveness of the scheme is demonstrated for the Lorenz and R\"ossler systems in numerical simulations and for the Chua and Rossler circuits in experiments. Functional-network analysis further shows that the two target systems are encoded by distinct dynamical patterns in the reservoir. These results extend multifunctional and parameter-aware reservoir computing, and provide a route to data-driven inference of multiple nonlinear systems using a single machine.