In this paper, the bifurcation analysis for Burgers mapping has been studied. The existence and stability of the fixed points of this map was derived. The conditions of existence for pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. The control of the map around stable NeimarkSacker bifurcation has been ac...

In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a simple example where the amplitude of limit cycles and the appearance of period-doubling bifurcations are controlled using a method derived from the frequency domain approach. In the second part, bifurcation theory is used to analyze the dynamical...

This paper discusses a problem of the Hopf bifurcation control for a mathematical model of intracellular calcium oscillations by calculating the curvature coefficient of limit cycle and the bifurcation control theory. We find that the appearance and disappearance of calcium oscillations in this system are due to the supercritical and subcritical Hopf bifurcation of equilibrium points, respectiv...

Cardiac arrhythmias have been closely linked to a variety of dynamic bifurcations such as Hopf bifurcation and period doubling bifurcation. This paper describes the utility of bifurcation control for suppressing pathological rhythms (such as cardiac alternans) in nonlinear models of cardiac electro-physiologic activities. Bifurcation control methods that deal with Hopf bifurcation and bordercol...

Introduction: Arteries are made up three layers; tunica intima, tunica media, and tunica adventitia. However, in some part of the artery this structure may change. The greatest change occurs at the junctions and bifurcations. In this regard, we decided to study the renal artery bifurcation just where the renal arteries divide into smaller arteries before entering the kidney. Methods: The struc...

A discrete-time periodic model with bang-bang feedback control is investigated. It is shown that each solution tends to one of four different types of limit 2-cycles. Furthermore, the accompanying initial regions for each type of solutions can be determined. When a threshold parameter is introduced in the bang-bang function, our results form a complete bifurcation analysis of our control model....

The normal forms and invariants of control systems with a parameter are found. Bifurcations of equilibrium sets are classified. The changes of properties such as controllability of the linearization or stabilizability near a bifurcation point of a control system are studied.

Period doubling bifurcation in buck converters is studied by using the harmonic balance method. A simple dynamic model of a buck converter in continuous conduction mode under voltage mode or current mode control is derived. This model consists of the feedback connection of a linear system and a nonlinear one. An exact harmonic balance analysis is used to obtain a necessary and sufficient condit...