Complex dynamic phenomena in space-invariant cellular neural networks

It is shown that first-order autonomous space-invariant cellular neural networks (CNNs) may exhibit a complex dynamic behavior (i.e., equilibrium point and limit cycle bifurcation, strange and chaotic attractors). The most significant limit cycle bifurcation processes, leading to chaos, are investigated through the computation of the corresponding Floquet's multipliers and Lyapunov exponents. It is worth noting that most practical CNN implementations exploit first-order cells and space-invariant templates: so far no example of complex dynamics has been shown in first-order autonomous space-invariant CNNs.