The use of Pyragas-Type controller proved interest in the stabilization of unstable periodic orbits. The stabilization problem of a balancing inverted pendulum on an horizontally moving cart by the use of such a controller is considered. The main objective of the paper is to propose delayed control law containing only proportional gains able to stabilize the inverted pendulum by avoiding the ex...

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using...

<abstract><p>In this paper, we use a semi-discretization method to explore predator-prey model with Michaelis-Menten functional response. Firstly, investigate the local stability of fixed points. Then, by using center manifold theorem and bifurcation theory, demonstrate that system experiences flip Neimark-Sacker at point when one parameters goes through its critical value. To illus...

The stability and Hopf bifurcation of gene expression models with a mechanism delayed state feedback are considered. An effective algorithm for the calculations on delay stable interval equilibrium point, direction, bifurcating periodic solution is also proposed. τ-decomposition strategy applied to tackle issue local stability, explicit formula provided. In addition, asymptotical behaviors solu...

In this paper, we investigate a delayed predator–prey model with prey refuge where the predator population eats according to Beddington–DeAngelis type functional response. Firstly, consider existence of equilibrium points. By analyzing corresponding characteristic equations, local stability trivial equilibrium, predator–extinction balance, and coexistence system are discussed, Hopf bifurcations...

Abstract: In this paper, a delayed ratio-dependent eco-epidemiological model with Holling type III functional response and two time delays is investigated.By regarding the delay as the bifurcation parameter, local stability of each equilibrium is discussed at the endemic equilibrium. By analyzing the corresponding characteristic equations, the conditions for existence of Hopf bifurcation for th...

This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lo...

In this study, a model of active control system with time delay feedback is investigated, and time delays were set in control loop. An efficient method was used to analyze the stability of the system. By solving the characteristic equation, the local stability and the existence of codimension one bifurcation (Hopf bifurcation and fold bifurcation) were obtained. Regarding the time delay as bifu...