We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that time delay has no effect on the ...

A neoclassical growth model is examined with a special mound-shaped production function. Continuous time scales are assumed and a complete steady state and stability analysis is presented. Fixed delay is then assumed and it is shown how the asymptotic stability of the steady state is lost if the delay reaches a certain threshold, where Hopf bifurcation occurs. In the case of continuously distri...

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...

In this paper, we derive the Hopf-Cole transformation to the diffusion approximation. We find the analytic solution to the one dimensional diffusion approximation and its Hopf-Cole transformation for a homogenous constant background medium. We demonstrate that for a homogenous constant background medium in one dimension, the Hopf-Cole transformation improves the stability of the inverse problem...

Totally geodesic property of the Hopf vector field. Abstract We prove that the Hopf vector field is a unique one among geodesic unit vector fields on spheres such that the submanifold generated by the field is totally geodesic in the unit tangent bundle with Sasaki metric. As application, we give a new proof of stability (instability) of the Hopf vector field with respect to volume variation us...

‎in this paper‎, ‎first we discuss a local stability analysis of model was introduced by p‎. ‎j‎. ‎mumby et‎. ‎al‎. ‎(2007)‎, ‎with $frac{gm^{2}}{m+t}$ as the functional response term‎. ‎we conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef‎. ‎next‎, ‎we consider this model under the influence of the time delay as the bifurcat...

We investigate Hopf bifurcations in a delayed Nicholson’s blowflies equation of neutral type, derived from the Gurtin–MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Global extension of local Hopf branches is established by combining a global Hopf bifurcation theorem with a Bendixson criteri...

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...