Parameter identification framework of nonlinear dynamical systems with Markovian switching

Area of Science:

• Dynamical Systems and Control Theory
• Computational Mathematics
• Stochastic Processes

Background:

• Deterministic models using ordinary differential equations (ODEs) struggle with real-world system complexities.
• Integrating Markov chains into nonlinear dynamical systems addresses environmental perturbations and random variations.
• Parameter estimation for ODEs with Markov chains remains an underexplored research area.

Purpose of the Study:

• To develop a comprehensive model for parameter estimation in nonlinear dynamical systems with Markovian switching.
• To bridge the research gap in modeling systems with discrete parameter switching.
• To enhance the realism and applicability of dynamical system models.

Main Methods:

• A machine discovery framework is presented for parameter estimation.
• The model combines a system of ordinary differential equations with a continuous-time Markov chain.
• This approach enables the representation of continuous systems with discrete parameter switching.

Main Results:

• The proposed framework effectively addresses the research gap in parameter estimation for Markovian switching systems.
• The integration of Markov chains captures time-varying dynamics influenced by environmental factors.
• The model provides more precise representations of complex dynamical systems.

Conclusions:

• The developed framework offers a more realistic and applicable approach to modeling dynamical systems with Markovian switching.
• This method enhances the ability to capture intricate, real-world system behaviors.
• It opens new avenues for research in parameter estimation for stochastic dynamical systems.