On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)

In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ's) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations

Synchronization of Chaotic Cellular Neural Networks based on Rossler Cells

Using and extending the approach in previous studies [2, 3] we demonstrate synchronization of two hyper chaotic cellular neural networks consisting of 25 cells governed by chaotic Rossler dynamics. We guarantee global asymptotic stability of the synchronization manifold by designing a nonlinear observer in such a way that the resulting error system is linear and time invariant. This linear error system is evaluated and a state feedback is designed to accomplish full state synchronization. Analytical as well as numerical simulation results are presented

Estimation of the basin of attractions of stable equilibrium points in CNNs

We present an approach to estimate the basin of attraction of stable equilibrium points in cellular neural networks (CNNs). The approach is based on the determination of the so called tree of regions connected with each stable equilibrium points described in our previous work (1997). The new contribution is connected with additional separation of the regions where the boundaries between different basins are located. The suggested separation with internal hyperplanes will help to estimate more precisely the boundaries between different basins, because the previous algorithm to obtain the trees could not give the exact description of the basin of attractions