In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given. Keyw...

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included. Keywords—Population model; Stability; Hopf bifurcation;...

OBJECTIVE To determine the position of the aortic bifurcation, angle of aortic-common iliac bifurcation in relation to the lumbar vertebra, diameter of distal aorta, length of common iliac, diameter of iliac at bifurcation in cadavers. MATERIALS AND METHODS The present study was done on 25 cadavers (16 males, 9 females) used for the dissection by 1st year MBBS students. The dissections were p...

Consider nonlinear dynamical systems modelled by parameterised differential and difference equations. When the values of the system parameters vary from those at which the system is currently operated, it can exhibit qualitative changes in behaviour and a steady-state may disappear or become unstable through a bifurcation [1, 2]. Bifurcation analysis is clearly useful and a bifurcation diagram ...

The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points flip and Neimark-Sacker , and so establish subor supercriticality of these bifurcat...

A predator-prey system with nonmonotonic functional response is considered. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and subcritical Hopf bifur...

BACKGROUND AND OBJECTIVE Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are ...