Predicting multistability of parameterized time-delay dynamical systems using reservoir computing

Area of Science:

• Nonlinear Dynamics
• Machine Learning
• Complex Systems Analysis

Background:

• Parameterized time-delay systems display multistability, where system behavior depends on initial conditions.
• This leads to multiple bifurcation diagrams and distinct evolutionary paths, complicating global behavior prediction.
• Understanding and predicting multistability is crucial for these systems.

Purpose of the Study:

• To employ reservoir computing for predicting multistability in parameterized time-delay systems.
• To demonstrate the efficacy of reservoir computing in capturing complex dynamics.
• To provide a framework for applying reservoir computing to intricate, multistable dynamical systems.

Main Methods:

• Utilized reservoir computing, a machine learning model for dynamics prediction.
• Trained the reservoir computing model with data from diverse parameter values and initial functions.
• Applied the model to two systems exhibiting dual Hopf and dual period-doubling bifurcation diagrams.

Main Results:

• Achieved prediction error rates of 0.215% for the dual Hopf bifurcation system.
• Achieved a highly accurate prediction error rate of 0.033% for the dual period-doubling bifurcation system.
• Demonstrated effective prediction of complex dynamics in parameterized time-delay systems.

Conclusions:

• Reservoir computing can effectively predict the complex dynamics of parameterized time-delay systems.
• The study establishes a framework for extending reservoir computing applications to multistable dynamical systems.
• This approach enhances the understanding of global behavior in systems with critical initial condition dependencies.