College of Computer Science and Mathematics

Discussion of a Doctorial Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Design of High-Dimensional Systems with Multiple Attractors and Its Applications “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday  4-10-2023

Doctorial Dissertation by student Zaidoon Shamil Hashim Mohammed Saleem

, under the supervision of    Assist. Prof. Dr. Saad Fawzi Jasim

  The high-dimensional nonlinear dynamic systems play a vital role in the development and promotion of many contemporary applications, especially in the fields of engineering and securing communications, due to the complex and unpredictable behaviors that these systems show.

In this thesis, two groups of hyperchaotic dynamical systems are generated. The first group includes expansion of 6D system derived from the 5D Lorenz system. While the second group includes a sequential control design from a 3D Liu chaotic system to a simple 7D hyperchaotic system by using the state feedback strategy and its combination with the coupling method. The most important dynamic properties of these systems are discussed, which include equilibrium points, stability, exponent and Lyapunov dimension, phase space, and the concept of coexistence. In addition to classifying the nature of these systems in terms of being dissipative or conservative systems depending on some of their parameters.

The efficiency of these proposed systems is evaluated through concrete engineering applications as follows:

• The first group: The proposed 6D system is applied in this group to control the robotic hand by the Inertial Measurement Unit (IMU). The working principle of this unit depends on measuring the degree of deviation of the sensor by a three-axis accelerometer. The problem faced by researchers in this field is determining the initial position (the zero position) that the IMU sensor encounters and reducing the impact of sensor reading deviation due to the sensor itself or a change in usage method. This problem is addressed by relying on the solution set of the equations of the dynamical system that enables the system to set the initial point and thus determining the position of the accelerometer and achieve four different movements on the robotic hand.
• The second group: Equivalent electronic circuits have been designed and implemented for the proposed systems in this group. The comparison of the results obtained through the oscilloscope reader by using the NI Multisim 14 program with the results of numerical simulations in the MATLAB R2021a program showed the effectiveness of these proposed systems.

Finally, the validity of the analytical results was confirmed by their compatibility with the numerical simulation using the Wolf Algorithm with the MATLAB R2021a program.

The scientific committee included the following members:

• Dr. Abdulghafoor Jasim Salim – Chairman .
• Dr. Mohammad Shami Hasso – Member.
• Prof. Dr. Thair Younis Thanoon – Member.
• Prof. Dr. Ahmed Mohammed Juma’a – Member.
• Prof. Dr. Lamiaa Hazim Saadoon – Member
• Prof. Dr. Saad Fawzi Jasim – Member and Supervisor