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On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

M. A. Budroni, M. Rustici, E. Tiezzi (2010)

Mathematical Modelling of Natural Phenomena

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...

On vanishing inflection points of plane curves

Mauricio Garay (2002)

Annales de l’institut Fourier

We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs f : ( ℂ 2 , 0 ) ⟶ ( ℂ , 0 ) which take into account the inflection points of the fibres of f . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

Borisov, Milen, Dimitrova, Neli (2010)

Serdica Journal of Computing

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

Laura Gardini, Viktor Avrutin, Michael Schanz, Albert Granados, Iryna Sushko (2012)

ESAIM: Proceedings

This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where...

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