Discussion of the Master’s Thesis Submitted to the College of Computer Science and Mathematics, Department of Mathematics, Entitled:

“Dynamic Simulation Tool for Chaotic Behavior in Biological Systems”

was defended in the discussion hall of the College of Computer Science and Mathematics at the University of Mosul on Sunday, Augst , 30, 2026.

supervised by  Prof. Dr. Maysoun Mal Allah Aziz

The thesis focuses on the development of mathematical models and dynamic simulation frameworks capable of representing complex chaotic behavior in biological systems, while accounting for nonlinearity, memory effects, and sensitivity to initial conditions. The study adopts the Rössler system as a baseline model and extends it to a fractional-order formulation using the Caputo derivative, followed by the development of four- and six-dimensional models to enhance the underlying dynamical complexity. The analysis includes equilibrium points, stability, dissipativity, Lyapunov exponents, and the Kaplan–Yorke dimension, together with the use of a genetic algorithm for parameter estimation based on electroencephalogram (EEG) data. The results demonstrate that the developed models are capable of generating chaotic and increasingly hyper chaotic dynamics, while achieving good agreement between real biological data and the numerical responses of the proposed models. The study concludes that integrating nonlinear modeling, fractional calculus, high-dimensional dynamical extensions, and optimization techniques provides an effective framework for simulating and analyzing complex behavior in biological systems.

The discussion committee consists of

• Prof. Dr. Abdul Ghafour Jasim Salem (Chairman)
• Prof. Dr. Omar Saber Qasim (Member)
• Asst. Prof. Dr. Azhar Abbas Mohammed (Member)
• Asst. Prof. Dr. Ahmed Intisar Ghaith (Member)
•  Asst. Prof. Dr. Mohammed Omar Shaaban  (Member)
• Prof. Dr. Maysoun Mal Allah Aziz (Member and Supervisor)