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

arXiv: https://arxiv.org/abs/2604.26632 · HTML: https://mlsanity.com/paper/2604.26632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks](https://mlsanity.com/paper/1502.04381/) (2015)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Parallel Machine Learning for Forecasting the Dynamics of Complex Networks](https://mlsanity.com/paper/2108.12129/) (2021)
- [Dynamical learning of dynamics](https://mlsanity.com/paper/1902.02875/) (2019)
- [Transfer learning of chaotic systems](https://mlsanity.com/paper/2011.09970/) (2020)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [Criticality in Reservoir Computer of Coupled Phase Oscillators](https://mlsanity.com/paper/2108.06395/) (2021)
- [Emergence of a stochastic resonance in machine learning](https://mlsanity.com/paper/2211.09955/) (2022)
- [Versatile Reservoir Computing for Heterogeneous Complex Networks](https://mlsanity.com/paper/2505.15219/) (2025)

## Abstract (arXiv)

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.