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Parameter identification framework of nonlinear dynamical systems with Markovian switching.

Zhikun Zhang1, Qiuhui Shen1, Xiangjun Wang1

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This study introduces a machine discovery framework for parameter estimation in nonlinear dynamical systems with Markovian switching. It enhances model realism by integrating ordinary differential equations with Markov chains for complex, real-world dynamics.

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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.