Cluster synchronization in inhomogeneous auto-oscillation medium. (Russian) Zbl 1048.37519
The considered model of distributed inhomogeneous auto-oscillation medium is described by the one-dimensional nonlinear partial differential equation
\[
a_t = i\omega(x)a + r(1 - | a| ^2)a + ga_{xx},
\]
where \(i = (-1)^{1/2}\), \(a(x, t)\) is the complex amplitude of oscillations, which depends upon time \(t\) and \(x\) is the spatial coordinate. The nonlinearity parameter \(r\) and the diffusion coefficient \(g\) are supposed constant. The frequency detuning is assumed linear along the spatial coordinate
\[
\omega(x) = x\Delta_{\max}/l,
\]
where \(l\) is the length of the system. Computer simulation reveals formation of frequency synchronization clusters. Cluster boundaries are studied.
Reviewer: Andrei Zemskov (Moskva)
MSC:
37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37M05 | Simulation of dynamical systems |
93C80 | Frequency-response methods in control theory |