The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcati...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azi...

We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are p...

The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1 : 1 (saddle-centre) and 1 : 2 (period-doubling). The twist, which is the derivative of the rotation number with respect to the action, is studied near these bifurcations. When the twist vanishes the nondegeneracy condition of the (isoenergetic) KAM theorem is not...

Eight balloon dilatations were performed in five patients (aged from 10 to 37 months) in whom supravalvar pulmonary stenosis developed after anatomical correction for complete transposition. The ratio of the maximum diameter of the inflated balloon to the narrowest pulmonary arterial diameter varied from 1.6 to 3.3. In three patients with an initial ratio of less than or equal to 2 dilatation w...

This study is intended to investigate the effect of various degree and position (pre-bifurcation post-bifurcation) stenosis on carotid artery hemodynamics trough realistic CFD numerical simulations with appropriate turbulence model. The blood rheological properties were assumed as incompressible Newtonian fluid. A 3 dimensional model a non-stenotic was used this investigation. Several tested. g...