I want to study complex network with chaotic oscillator (with second or third order). All the tools available for data visualization and analysis does not included the dynamics of the node. I want model a complex network where each node of the network become having chaotic dynamics.
You may try a neuronal network of the form:
dxi/dt=K Aij F(xj)-xi
where F is a sigmoid function (for instance tanh), Aij is a random matrix where Aij follows a normal law of mean 0 and variance 1/N, and N is the number of nodes.
For N sufficiently large, the system will exhibit chaotic behavior when K becomes greater than 1.
Dear Suresh,
first build the topology of your complex network, e.g. a small world network. Now, at each node place a chaotic oscillator, e.g. Rossler in a chaotic regime. Now couple the oscillators according to your topology and, for instance, use only the x variable to do so. That means the first equation of the Rossler oscillator that is at node i (assuming that your topology says that such a node is connected to node j) should have an extra term say Kc(x_j-x_i). If you start with no coupling Kc=0, then all the oscillators are chaotic, but you do not have a network... just a bunch of isolated oscillators. Now start gradually increasing Kc. At a certain point you might find that the oscillators are phase synchronized. In such a situation, you will typically have high-dimension dynamics, perhaps chaotic. If you reach complete sync (say, at large values of Kc) then you whole network will behave as a single chaotic oscillator and I don't think that is what you want.
Hope this was helpful.
Cheers.
Luis
Dear Luis,
Thank you very much. I need exactly what you said. I understand it clearly.
Another part of my question is that, is there any tool like cytoscape or software available to do this? I can do the fortran code however it will be convenient if there are tools for this.
Dear Siess,
Thank you very much. Are there any tools available to do this?
I personally would write a script to generate a string containing the set of equations corresponding to the chosen system (topology and dynamics) for instance in modelica syntax and then launch simulations with a modelica simulator, open modelica for instance.
- Badges
- Science topic
- Similar topics
- Human-Computer Interaction
- Collaboration