Some results on the dynamics generated by the Bazykin model

A predator-prey model formerly proposed by A. Bazykin et al. [Bifurcation diagrams of planar dynamical systems (1985)] is analyzed in the case when two of the four parameters are kept fixed. Dynamics and bifurcation results are deduced by using the methods developed by D. K. Arrowsmith and C. M. Place [Ordinary differential equations (1982)], S.-N. Chow et al. [Normal forms and bifurcation of planar fields (1994)], Y. A. Kuznetsov [Elements of applied bifurcation theory (1998)], and A. Georgescu [Dynamic bifurcation diagrams for some models in economics and biology (2004)]. The global dynamic bifurcation diagram is constructed and graphically represented. The biological interpretation is presented, too

Approximation of pressure perturbations by FEM

In the mathematical problem of linear hydrodynamic stability for shear flows against Tollmien-Schlichting perturbations, the continuity equation for the perturbation of the velocity is replaced by a Poisson equation for the pressure perturbation. The resulting eigenvalue problem, an alternative form for the two - point eigenvalue problem for the Orr - Sommerfeld equation, is formulated in a variational form and this one is approximated by finite element method (FEM). Possible applications to concrete cases are revealed.Comment: Presented at the 10th Conference on Applied and Industrial Mathematics - CAIM 2002, Pitesti and Mioveni, Romania, October, 2002; Scientific Bulletin of the Pitesti Universit

Degenerated Hopf bifurcation in the Fitzhugh-Nagumo system. 2. Bautin bifurcation

The results on the Hopf bifurcation obtained in [1] are completed with those concerning the degenerated Hopf bifurcation of Bautin type. They are deduced by normal forms technique and concern a biodynamical system related with Van der Pol oscillator. Numerical investigations carried out by methods from [2] are also reported