  Optimization techniques play a crucial role in estimating parameters and
state information for nonlinear systems. However, some critical aspects of
these problems have received little attention in previous research. In this
paper, we address this gap by exploring optimization techniques for parameter
estimation in nonlinear system modeling, with a focus on chaotic dynamical
systems. We introduce three optimization methods - a gradient-based iterative
algorithm, the Levenberg-Marquardt algorithm, and the Nelder-Mead simplex
method - that transfer the complex nonlinear optimization problem into a
simpler linear or nonlinear one. We apply these methods to determine the
parameters of nonlinear systems, presenting a numerical example to demonstrate
their effectiveness. Our results show that the Nelder-Mead simplex method is
particularly effective in estimating the parameters of nonlinear systems and
has the potential to be a valuable tool in various fields that require
nonlinear system modeling. Overall, our study contributes to the understanding
and improvement of optimization techniques for parameter estimation in
nonlinear system modeling, which has implications for a wide range of
applications in science and engineering.
