الفهرس | Only 14 pages are availabe for public view |
Abstract The main goal of this thesis is to study the dynamics of a Riccati differential equation with perturbed delay and its fractional-order equation and introduce a new concept of perturbed delay. The study focuses on understanding the behaviour of the solution through the application of analytical techniques to investigate the existence and uniqueness of the solution and its continuous dependence on initial conditions. Analyses of Hopf bifurcations and the local stability of fixed points are conducted. Utilising piecewise constant arguments, the discrete system is generated in order to simulate the behaviour of the system under consideration. The local stability analysis of the fixed points of the discrete system is presented. Numerical simulations using phase diagrams, Lyapunov exponents, and bifurcation diagrams are illustrated. This helps confirm our study and unearth more complex dynamics. The results of theoretical investigations of the Riccati differential equation with delay, its fractional-order equation, and their perturbed equations are compared. |