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University of Plymouth | Centre for Theoret. and Comput. Neuroscience | Home
Example 3: Coupled Roessler Oscillators
This example implements a network of Roessler oscillators under various coupling conditions. The Roessler oscillator is a nonlinear oscillator that shows chaotic trajectories under certain parameter conditions. When coupled homogeneously (through the mean-field), these oscillators can show some "weak" form of synchronization, where the individual elements are not perfectly synchonous, but nonetheless to some degree oranized into a collective oscillation. This phenomenon has been first described by Pikovsky and Kurths in Phys Rev E a couple of years ago. Beside meanfield couplings (all to all with equal strength) the simulation also lets you select random or diffuse couplings.The example demonstrates, how you may use the Runke-Kutta driver that comes with the felix package in order to solve ordinary differential equations. Some new types of data views are also introduced. Below you find a picture of the graphical user interface. Explanations are given below the figure.
The bottom frame shows the usual main control frame comprising sliders specific for the present model system. "delta omega" sets the frequencies of the oscillator to different values, the more different the higher the value of the slider; a value of zero corresponds with identical oscillators. "a" is a parameter that controls the Roessler oscillators. You can also see 3 "Switches", which allow to select between different coupling schemes: "mean" (fully connected), "diffusive" (some kind of nearest neighbor coupling), and "random" (Gaussian with certain mean and variance).
The different viewing frames display dynamic variables of the simulation in various formats. Right on top of the main control frame the first and second variable of an individual oscillator is shown over time. Which oscillator is displayed can be set in a popup window that comes up if the buttons "x1" or "x2" are pressed. The "signal" frame shows the x1-variables of all oscillators as a raster plot over time. Right of it you can see a "Plot". This type of view plots pairs (x1(t), x2(t)) in a 2D coordinate system joined by lines. Which element is displayed and the x and y ranges can again be controlled in popup windows. The upper most view again is a "Plot" but now for the averages X1 and X2 over the whole set of oscillators, respectively. These can be interpreted as order parameters of the system: In incoherent states they are (almost) zero, in coherent states they are finite and may become as big as the variables in single oscillators.
Downloads
Statically linked executable (Right-click and store using "Save Link Target .." or similar. Start by clicking on it after download.)
Environment file (Put this file into a subdirectory "env" in the directory of the executable, which will then start with appropriate parameters.)
Shared library executable (Right-click and store using "Save Link Target .." or similar.)
Note 1: If the statically linked executable does not start, you might need to make it executable by setting the right permissions. It might also be that you don't have all necessary libraries (none of which is, however, very exotic). Try "ldd rros" on the command line to see if something is missing.
Note 2: To run the shared library executable you need to install the felix runtime libraries; to compile the source code you need to install in addition the felix development tools. See HERE for more info.
© 2004 by -thowe-