UMIST The use of boundary locus plots in the identiication of bifurcation points in numerical approximation of delay diierential equations Abstract We are interested in nonlinear delay diierential equations which have a Hopf bifurcation. We assume zero is a steady state for the problem, and so a Hopf bifurcation point lies on the boundary of the region of asymptotic stability for the zero solut...

The solution manifold of the system of nonlinear differential equations representing a BWR needs to be examined to understand its dynamical behavior. In particular, stable or unstable fixed points and stable or unstable oscillatory solutions (or turning points/saddle node bifurcations) are of paramount interest. In this framework integrated BWR (system) codes and simplified BWR models (reduced ...

We study the dynamics of a model of white-blood-cell (WBC) production. The model consists of two compartmental differential equations with two discrete delays. We show that from normal to pathological parameter values, the system undergoes supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles. We characterize the steady states of the system and perform a bifurcation analy...

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location i...

In this paper, we study the dynamical behaviors of a three-node recurrent neural network model with four discrete time delays. We study several types of bifurcation, and use the method of multiple time scales to derive the normal forms associated with Hopf-zero bifurcation, non-resonant and resonant double Hopf bifurcations. Moreover, bifurcations are classified in two-dimensional parameter spa...

Abstract. We study the appearance of a novel phenomenon for linearly coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf b...

In this article we study periodic solutions of a mathematical model for brain tumor virotherapy by finding Hopf bifurcations with respect to a biological significant parameter, the burst size of the oncolytic virus. The model is derived from a PDE free boundary problem. Our model is an ODE system with six variables, five of them represent different cell or virus populations, and one represents ...