SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Exponentially long transient oscillations in a class of cooperative cellular networks

B.M. Garay, M. Forti, M. Koller and L. Pancioni

Abstract
The real-time processing capabilities of CNNs are inherently related to the fast convergence time of the solutions toward the asymptotically stable equilibria. A typical requirement is that the settling time should not exceed a few (or at most ten) cell time constants. We report on a class of completely stable nonsymmetric cooperative CNN rings whose solutions display unexpectedly long transient oscillations for a wide set of initial conditions and interconnection parameters. Numerical simulations show that the oscillations can easily last hundreds of cycles, and thousands of cell time constants, before settling to a steady state, thus possibly impairing their real-time processing capabilities. Laboratory experiments on a discrete-component prototype of the CNN ring shows that the long oscillation phenomenon is physically robust with respect to the non-idealities of the circuit implementation. Finally, asymptotic estimates on the duration of the transients are given.

Organized by         Universidad de Valladolid     IMUVA