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...

Background and Objective: Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are...

We consider the delayed feedback control method for stabilization of unstable rotating waves near a fold bifurcation. Theoretical analysis of a generic model and numerical bifurcation analysis of the rate-equations model demonstrate that such orbits can always be stabilized by a proper choice of control parameters. Our paper confirms the recently discovered invalidity of the so-called "odd-numb...

background and objective: cerebral arteriovenous malformation (cavm) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in arteriovenous malformation patients. the vessel geometry in cavm patients are...

The quadratic and cubic normal forms of discrete time nonlinear control systems are presented. These are the normal forms with respect to the group of state coordinate changes and invertible state feedbacks. We introduce the concept of a control bifurcation for such systems. A control bifurcation takes place at an equilibrium where there is a loss of linear stabilizability in contrast to a clas...

Stationary bifurcation control is studied under the assumption that the critical zero eigenvalue is uncontrollable for the linearized system. The development facilitates explicit construction of feedback control laws that render the bifurcation supercritical. Thus, the bifurcated equilibria in the controlled system are guaranteed stable. Both pitchfork bifurcation and transcritical bifurcation ...

Bifurcation tailoring is a method developed to design control laws modifying the bifurcation diagram of a nonlinear dynamical system to a desired one. In its original formulation, this method does not account for the possible presence of constraints on state and/or manipulated inputs. In this paper, a novel formulation of the bifurcation tailoring method overcoming this limitation is presented....

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision ...

This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Exp...