This paper deals with the dynamics of food web consisting of two logistic preys and a variable harvesting predator of Modified LeslieGower type. The existence of Hopf bifurcation analysis with varying key parameter is investigated.

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...

In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis. Keywords—Physiological...

In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtaine...

This paper concerns the control design of a PID controlled gimbals suspension gyro, whose parameters are determined by using bifurcation theory. The non-linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes. Considering a PID controller with constrained integral action, it is shown that depending on different values of the maximum allowed integral action a ...

A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is sin θ, a bifurcation diagram conjectured by Kuramoto is rigorous...

forming limit diagram (fld) is an important diagram by which the formability of sheet metals is studied. strain rate is a very effective parameter influencing the fld which is, in turn, influenced by the forming velocity. in this work, forming limit diagram for st14 was investigated both experimentally and numerically. in addition, the effect of forming velocity was studied and the experiments ...

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits, which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension 1. Several bifurcation scenarios are described in detail. They are ...

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yosida operator. The theorem is proved using the center manifold theory for nondensely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation resul...