Journal of Al-Qadisiyah for Computer Science and Mathematics

This study aims to analyze the dynamics of trajectories in a system of Van der Pol with the coupled oscillator. The control parameters considered are damping and coupling strength. We focus on study the behaviour of this system within a specific small invariant subspace. It is used phase difference to reduce the dimension of this system into two dimensions. Then, the Jacobian matrix is computed eigenvalues in order to determine the stability of equilibrium point. this work specifically discovers the effects the damping and coupling strength parameters to emerge synchronization states. additionally, it investigates how change the value of damping parameter influence on the system's energy.

In the current study, the researcher explores and delineates several characteristics of S*-I-open groups, and pre*-I-open groups within ideal topological spaces. Additionally, we establish connections between pre*-I-open groups, and S*-I-open groups in these spaces. Ultimately, the researcher achieves a decomposition of continuity, enhancing the understanding of how these sets interact and contribute to the broader topological framework

Generalized exponential convexity has been one of the most important concept in generalized convex analysis, not only because of its structural properties used to relax convexity assumptions, but also because of its various applications in applied fields, especially in mathematics and optimization theory. In this paper, a class of two types of generalized convex functions is introduced, namely exponential semiE-preinvex functions and exponentially quasi semi E-preinvex functions. Several insights are presented, starting with providing a necessary and a sufficient condition for a function to be semi E-preinvex function. Also, several general algebraic properties of these functions are estalished. Moreover, various characterizations and conditions are provided to relate these functions to their levels and graph sets. Finally, some optimality properties for nonlinear optimization problems with exponentially E-preinvex functions, exponentially semi E-preinvex functions and exponentially quasi semi E-preinvex functions are shown. Two examples are presented to illustrate the new functions developed in this work.