A Hybrid Cellular Neural Network (CeCNN) Structure

This paper demonstrates a complete mathematical and geometric analysis of novel hybrid Cellular Neural Network (CeCNN) structure. The presented CeCNN model unites the local connectivity properties of traditional Cellular Neural Networks (CNN) with enhanced nonlinear dynamics through a hybrid cell architecture. The complete state-space representation is derived using first-order ordinary differential equations, and then network topologies and their geometric properties are discussed in detail. Both feedback as well as feedforward templates are included in the mathematical model, providing a basis for processing of complex spatiotemporal patterns. Stability analysis based on Lyapunov theory is given. It is also shown that a certain convergence condition must be satisfied, derived from the above stability analysis in order to show convergence by simulating various examples. Simulation results are presented, showing the effectiveness of the new model in image processing and pattern recognition tasks. The implementation is verified through Python simulations on Google Colab platform.