javad alidousti

In the present study, we analyze dynamics and bifurcations of a discrete-time    Hopfield neural network  based on two neurons and the same time delay. We determine stability and bifurcations of the system consisting flip, pitchfork and Neimark-Sacker  bifurcations. The normal form coefficients for the all bifurcations are calculated using reducing to the corresponding  center manifold, then these coefficients are  numerically obtained using MatContM. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.

This paper studies the dynamical behavior of a discrete-time predator-prey analytically and numerically. The conditions and the critical coefficients for the transcritical, flip (period-doubling), and Neimark-Sacker are computed by using the center manifold and normal form technique. Besides, codimension-two bifurcations including strong resonances 1:2, 1:3, and 1:4  have been achieved. The numerical simulation and continuation method, not only confirm our analytical results but also reveals richer dynamics of the model, especially in the higher iteration.

In this paper, the local stability of the endemic equilibrium and existence of a Hopf bifurcation in a Susceptible-ExposedInfected-Recovered (SEIR) delayed mathematical model for COVID-19 pandemic are investigated. By using time-delay as a bifurcationparameter, the associated characteristic equation is analyzed to reveal dynamics of the model. Finally, numerical simulations areperformed with suitable parameters choice to illustrate the theoretical results of the model.

In this paper, we study the effect of delayed feedback on the dynamics of a three-dimensional chaotic dynamical system and stabilize its chaotic behavior and control the respective unstable steady state. We derive an explicit formula in which a Hopf bifurcation occurs under some analytical conditions. Then the existence and stability of the Hopf bifurcation are analyzed by considering the time delay $ \tau $ as a bifurcation parameter. Furthermore, by numerical calculation and appropriate ascertaining of both the feedback strength $ K $ and time delay $ \tau $, we find certain threshold values of time delay at which an unstable equilibrium of the considered system is successfully controlled. Finally, we use numerical simulations to examine the derived analytical results and reveal more dynamical behaviors of the system.

‎The present study aims are to analyze a delay tumor-immune fractional-order system to describe the rivalry among the immune system and tumor cells. Given that the dynamics of this system depend on the time delay parameter, we examine the impact of time delay on this system to attain better compatibility with actuality. For this purpose, we analytically evaluated the stability of the system’s equilibrium points. It is shown that Hopf bifurcation occurs in the fractional system when the delay parameter passes a certain value. Finally, by using numerical simulations, the analytical results were compared to the numerical results to acquire several dynamical behaviors of this system.

In this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator-prey oscillations. Therefore, antipredator behaviour helps the prey population to resist predator aggression.

‎In this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of Lyapunov‎ ‎method‎. ‎To examine the obtained results‎, ‎we employe the developed techniques on test examples‎.