Parameter identification framework of nonlinear dynamical systems with Markovian switching

Extensive research has been conducted on models of ordinary differential equations (ODEs), yet these deterministic models often fail to capture the intricate complexities of real-world systems adequately. Thus, many studies have proposed the integration of Markov chains into nonlinear dynamical systems to account for perturbations arising from environmental changes and random variations. Notably, the field of parameter estimation for ODEs incorporating Markov chains still needs to be explored, creating a significant research gap. Therefore, the objective of this study is to investigate a comprehensive model capable of encompassing real-life scenarios. This model combines a system of ODEs with a continuous-time Markov chain, enabling the representation of a continuous system with discrete parameter switching. We present a machine discovery framework for parameter estimation in nonlinear dynamical systems with Markovian switching, effectively addressing this research gap. By incorporating Markov chains into the model, we adeptly capture the time-varying dynamics of real-life systems influenced by environmental factors. This approach enhances the applicability and realism of the research, enabling more precise representations of dynamical systems with Markovian switching in complex scenarios.