Sine Diffusion Model for Nonlinear Dynamical Systems

A dynamical system is a concept in mathematics where a fixed rule describes how a part in a geometrical space depends on time. Dynamical systems are mathematical objects used to model physical phenomena whose state changes over time. The realizations from these systems are usually corrupted by random noise. Hence, the importance of modelling such systems as a stochastic process. This study considered modelling the systems using stochastic differential equations which is a diffusion model. The study proposed a logarithmic mean reverting sine diffusion (LMRSD) process for modelling dynamics of nonlinear dynamical systems. Two empirical data were used for illustrations and the Euler scheme in R statistical package was adopted for the numerical estimations of the model parameters. The proposed model was compared with existing models and the study revealed that the proposed model performs well than the existing models with lowest values of the information criterion. (