Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, and disease spread. We present an efficient approach for system identification based on correlation techniques for linear temporal systems that extended to spatiotemporal IDE-based models. The method is derived from the average (over time) spatial correlations of observations to calculate closed-form estimates of the spatial mixing kernel and the disturbance covariance function. Synthetic data are used to demonstrate the performance of the estimation algorithm

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

A Numerical Study of the Complex Lorenz System as a Dynamical Model

A nonlinear dynamical system is a mathematical model for a portion of the physical world where continuous components are interacting with each other. Such systems are complex, and it is difficult to predict how they will react towards changing the driving parameters and initial conditions. \\ This dissertation is concerned with the numerical aspect of controlling the Lorenz system that studies the production of the magnetic field in sunspots. The study aims to do this by applying different approaches to the system