Continuous-time Cellular Neural Networks Research Articles

Associative memories based on continuous-time cellular neural networks designed using space-invariant cloning templates

Associative memories are brain-style devices designed to store a set of patterns as stable equilibria such that the stored patterns can be reliably retrieved with the initial probes containing sufficient information about the patterns. This paper presents a new design procedure for synthesizing associative memories based on continuous-time cellular neural networks with time delays characterized by input and output matrices obtained using two-dimensional space-invariant cloning templates. The design procedure enables hetero-associative or auto-associative memories to be synthesized by solving a set of linear inequalities with few design parameters and retrieval probes feeding from external inputs instead of initial states. The designed associative memories are robust in terms of design parameter selection. In addition, the hosting cellular neural networks are guaranteed to be globally exponentially stable. Simulation and experimental results of illustrative examples and Monte Carlo tests demonstrate the applicability and superiority of the methodology.

Horseshoe and topological entropy estimate of a class of three-dimensional cellular neural networks

Chaos in a class of three-dimensional continuous time cellular neural networks is investigated. Numerical experiments show that this class of cellular neural networks can display chaotic attractors and limit cycles for different parameters. By virtue of topological horseshoes theory in dynamical systems, a rigorous computer-assisted verification for chaotic behavior of the neural network is presented for certain parameter. Topological entropy estimate of the neural network is also given in terms of the Poincaré map.

Exponential stability of continuous-time and discrete-time cellular neural networks with delays

Convergence characteristics of continuous-time cellular neural networks with discrete delays are studied. By using Lyapunov functionals, we obtain delay independent sufficient conditions for the networks to converge exponentially toward the equilibria associated with the constant input sources. Halanay-type inequalities are employed to obtain sufficient conditions for the networks to be globally exponentially stable. It is shown that the estimates obtained from the Halanay-type inequalities improve the estimates obtained from the Lyapunov methods. Discrete-time analogues of the continuous-time cellular neural networks are formulated and studied. It is shown that the convergence characteristics of the continuous-time systems are preserved by the discrete-time analogues without any restriction imposed on the uniform discretization step size.

An Active Contour Algorithm for Continuous-Time Cellular Neural Networks

A CNN-based algorithm for image segmentation by active contours is proposed here. The algorithm is based on an iterative process of expansion of the contour and its subsequent thinning guided by external and internal energy. The proposed strategy allows for a high level of control over contour evolution making their topologic transformations easier. Therefore processing of multiple contours for segmenting several objects can be carried out simultaneously.

Relation between template spectrum and stability of cellular neural networks with delay

Some results are presented concerning the dynamic behaviour of reciprocal, continuous-time cellular neural networks (CNNs) in the presence of cell delay. Symmetrically connected CNNs with cell delay can oscillate if the delay is larger than a critical value depending on the cloning template. Empirical formulas are given relating the critical delay to the template Fourier transform. These results can be used as design guidelines taking into account the delays introduced in hardware VLSI implementations.