9478

Rabinovich-Fabrikant Equations

The Rabinovich–Fabrikant equations form a set of coupled, nonlinear, first-order differential equations given by:
,
,
.
This Demonstration lets you explore the solutions to this system. The system parameters, and , are modified in this Demonstration by adding a parameter scaling factor . By varying these system parameters as well asthe parameter scaling factor and the initial positions , interesting dynamical events, including chaotic motion, periodic motion, limit cycles, and attractors can be observed in the generated trajectories. These trajectories can be viewed either in three-dimensional space or as projections in two-dimensional planes by changing the plot style. The plot in three dimensions is colored using a gradient in the direction.

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DETAILS

Programming ideas on how to implement the plot style switching were taken from the Demonstration "A Study of the Dynamic Behavior of a Three-Variable Autocatalator" by Housam Binous and Zakia Nasri.
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