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...

In this paper, we review some recent results on the nonlinear dynamics of delayed differential equation models describing interaction between tumor cells and effector immune system, in which delays represent times necessary for molecule production, proliferation, differentiation cells, transport, etc. First consider a tumor-immune system model with single delay pres...

A three-stage-structured prey-predator model with discrete and continuous time delays is studied. The characteristic equations and the stability of the boundary and positive equilibrium are analyzed. The conditions for the positive equilibrium occurring Hopf bifurcation are given, by applying the theorem of Hopf bifurcation. Finally, numerical simulation and brief conclusion are given.

The diffusive Lotka–Volterra predator–prey system with two delays is reconsidered here. The stability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations, and our results complement earlier ones. We also obtain that in a special case, a Hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system. © 2011 ...

The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem. Keywords—Hes1, Hopf bifurcation, time delay, transcriptional repression loop

Based on analytic calculations we identify the local structures which changes the parity of the global traveling wave states on its either sides. We establish the fact that competition of Turing and Hopf modes and multi-stability is not an essential ingredient for the generation of asynchronous one dimensional wave rather, close to a purely Hopf instability boundary and well in the region where...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out. Keywords—Nicholson,s blowflies model; Stability; Hopf bifurcation; Delay.

this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hop...