Multi-amplitude and multi-phase synchronization phenomena in nonlinear large-scaled oscillating cellular neural networks

The synchronization is very important technology in the field of Cellular Neural Networks (CNNs) due to its various applications from the biological, environmental to communication points of view. This paper deals with the parametric synchronization phenomena in large-scaled oscillating CNN. When we determine adequate parameters for the amplitude and frequency in the large-scaled oscillating CNNs with non-oscillating cells, the CNN oscillates in various ways depending on their conditions. In this paper, we have exhibited that both multi-amplitude and multi-phase synchronization are generated by their parameters. To demonstrate them, we simulated multi-dimensional CNN of 4 × 4 (16 cells), 8 × 8 (64cells) and 16 × 16 (256 cells) and checked the synchronization phenomena. Each cell has an inductor L, a capacitorC and a complex nonlinear conductance as i = f(v). We find that the synchronization phenomena are similarly occurred from the small networks to the larger one. We give a basic theoretical viewpoint for interesting numerical experiment results for the synchronization phenomena in this paper.