This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigration parameter on prey population. Particularly, we study existence local asymptotic stability unique positive fixed point. Furthermore, conditions for bifurcation in are derived. In addition, it shown that goes through period-doubling by using theory center manifold theorem. Eventually, nume...

This paper deals with a three-species ecological system with time delay and harvesting. Sufficient conditions guaranteeing the local stability and the occurrence of Hopf bifurcation for the system are obtained. Further, the properties of Hopf bifurcation are investigated using the center manifold theorem and normal form theory. Computer simulations are carried out to illustrate the theoretical ...

In this talk we will first describe how the clocks synchronization problem can be modeled as a consensus algorithm for heterogeneous double integrators. We show two possible implementations of this consensus based clocks synchronization. The dynamics of one of these can be described as a discrete time nonlinear system, which is a perturbation of the linear system. Hence, using the center manifo...

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...

We define center manifold as usual as an invariant manifold, tangent to the invariant subspace of the linearization of the mapping defining a continuous dynamical system, but the center subspace that we consider is associated with eigenvalues with small but not necessarily zero real parts. We prove existence and smoothness of such center manifold assuming that certain inequalities between the c...

This paper, according to the process of capital return, establishes a differential dynamics model investment with two time delays. When both delays are zero, it is proved that positively invariant, uniformly bounded, and globally asymptotically stable by using comparison principle Bendixson–Dulac theorem. at least one delay not Hopf bifurcation theorem, conditions local asymptotic stability exi...