Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems is linked to degeneracies in the system zero dynamics. Accordingly, the obvious remedy is to change the system input-output structure, but there are other possibilities as well. In this paper we summarize the main results connecting bifurcation beha...

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback...

We introduce a method for tracking nonlinear oscillations and their bifurcations in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system nor the ability to set its initial conditions. Instead it relies on feedback stabilizability, which makes the approach applicable in an experiment. This is demonstrated with a proofof-concept computer experiment...

We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay tau and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf st...

We derive and analyse a deterministic model for the transmission of malaria disease with drug resistance in the infectives. Firstly, we calculate the basic reproduction number, R, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation, with this occurrence, the classical epidemiological requirement for effective eradication of malaria, R <...

Abstract. In this paper, we first build up a Westwood+ TCP congestion control model with communication delay in mobile cloud computing networks. We then study the dynamics of this model by analyzing the distribution ranges of eigenvalues of its characteristic equation. Taking communication delay as the bifurcation parameter, we derive the linear stability criteria depending on communication del...

Using the predictor-corrector scheme, the fractional-order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional-order diffusionless system for variation of the single control parameter is determined. The route to chaos is by period-doubling bifurcation in this fractional-order system, and some typical bifurcations are observed, such as the flip ...

A bstract |This paper reexamines the conventional currentmode control strategy as applied to dc/dc converters in the ligh t of \avoiding bifurcation". This alternativ eviewpoint permits convenien t selection of parameter values to guarantee stable operation. Slope compensation is viewed as a means to k eep the system suÆciently remote from the rst bifurcation point. It is shown that excessiv e ...

An unusual bifurcation to time-periodic oscillations of a class of delay differential equations is investigated. As we approach the bifurcation point, both the amplitude and the frequency of the oscillations go to zero. The class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations. B...

A simplified model of a container crane subject to a delayed feedback is investigated. The conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined. It is shown that a subcritical Hopf bifurcation to unstable oscillations cannot be ruled out and the undesired coexistence of stable large amplitude oscillations and a stable equilibrium endangers the robustness of ...