Visualization of Mixed Mode Oscillations

Lukas Mroz, Eduard Gröller, Alexandra Milik, Peter Szmolyan

project duration: 1995-1997

Mixed-mode oscillations are a phenomenon quite often encountered in chemical systems. They owe their name to the alternating large and small amplitute heigths in the observed time series. A second characteristic feature of mixed-mode oscillations are the alternating chaotic and periodic responses occuring in special sequences as a parameter is varied. One of the simplest sets of kinetic equations exhibiting misxed mode oscillations is the 3-dimensional autocatalator. This model consists of three nonlinearly coupled ordinary differential equations. The pictures below show the evolution of this system for a whole set of initial conditions in the part of phase space where the complex behaviour of the system is generated. As the set of initial conditions is a line in phase space this gives a surface. A second 'inverse' surface is generated by simulating a line of initial conditions backwards in time. The intersection of the two surfaces plays a crucial role in explaining the complex dynamics of this system.

System with with noise texture(98 K)

System and Inverse System (Example 1)(399 K)

System and Inverse System (Example 2)(229 K)

This page is maintained by Eduard Gröller. It was last updated on November 20, 1998.
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