in this paper, a three dimensional mathematical model for htlv-1infection with intracellular delay and immune activation delay is investigated.by applying the frequency domain approach, we show that time delays candestabilize the ham/tsp equilibrium, leading to hopf bifurcations and sta-ble or unstable periodic oscillations. at the end, numerical simulations areillustrated.

The effect of distributed delays with strong kernel in the dynamics in three-neuron BAM neural network model is studied. Instead of destabilization phenomena this neural systems become asymptotically stable through Hopf bifurcation with the gradual increment of mean delay. Existence of Hopf bifurcation is studied in frequency domain. Direction and stability of Hopf bifurcating periodic solution...

In this article, we develop a modified version of the graphical Hopf bifurcation theorem for capturing smooth oscillations of delay differential equations with distributed delays. Our approach relies on a simple interpretation of the effect of the distributed delay based on the Laplace transform. The theoretical results are illustrated with an example of neural networks.

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...

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

the present paper deals with a toxin producing phytoplankton (tpp)-zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. in the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. after that tpp-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both popu...

The main objective of this addendum to the mentioned article [49] by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to comment and list some related literatures, without any intention to provide a complete survey. For steady state PDE bifurcation problems, the often used c...

We study the symmetries of periodic solutions obtained from Hopf bifurcation in systems with finite abelian symmetries. The H mod K Theorem gives necessary and sufficient conditions for the existence of periodic solutions with spatial symmetries K and spatio-temporal symmetries H in systems with finite symmetry group Γ. Our main result, the Abelian Hopf H mod K Theorem, gives necessary and suff...

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifu...

A simple comparison of the areas of the sciences in which DAEs are involved with those in which examples of Hopf bifurcation in ODEs arise (see Thompson and Stewart (1986) and the references therein) reveals a considerable overlap and suggests that an appropriate variant of the Hopf bifurcation theorem should be available in the DAE setting. In this chapter, we show that, indeed, a generalizati...