Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2005-05-18
Phys. Rev. E 72, 066217 (2005)
Nonlinear Sciences
Chaotic Dynamics
14 pages, 13 figures, important changes (title changed, discussion, figures, and references added)
Scientific paper
10.1103/PhysRevE.72.066217
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if $\tau_{ij}$ are random enough the array synchronizes in a spatially homogeneous steady state. Here we study this behavior by comparing the dynamics of a map of an array of $N$ delayed-coupled maps with the dynamics of a map with $N$ self-feedback delayed loops. If $N$ is sufficiently large, the dynamics of a map of the array is similar to the dynamics of a map with self-feedback loops with the same delay times. Several delayed loops stabilize the fixed point, when the delays are not the same; however, the distribution of delays plays a key role: if the delays are all odd a periodic orbit (and not the fixed point) is stabilized. We present a linear stability analysis and apply some mathematical theorems that explain the numerical results.
Marti Arturo C.
Masoller Cristina
Ponce Marcelo
No associations
LandOfFree
Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-710388