On Circuits Exhibiting Unstable Spatial Modes | Chapter 6 | Current Research Progress in Physical Science Vol. 8

Pattern formation and modelling is a vast domain of research with applications in various engineering, physical, biological, chemical, etc. areas. Pattern generation can be defined and modelled as the process of reaching a stable nonuniform equilibrium point in a network or array of interconnected cells (usually) exhibiting certain homogeneities starting from a given deterministic or random input signal. In what follows, aspects regarding the dynamics and pattern formation in a couple of particular circuit architectures able to exhibit unstable modes, are discussed. A unifying approach for these types of neural-like circuits is based on unstable spatial modes using the mode decoupling technique. An important objective is that of showing the way the dynamics can be prescribed by using the relationship between the extended graph Laplacian and nodal equations or state equations. Thus, the possibility of designing a spatial comparator that can extract the sign of a prescribed spatial mode has been analyzed. The mode is supposed to be contained in a spatial signal introduced as initial condition, using unstable circuits for which that mode is associated with a right half plane eigenvalue. The dynamics have been theoretically analyzed and illustrated with simulations, including CMOS technology realizations.

The main results reported in this chapter have been published. Simulations including a CMOS realization confirmed the analytical results, as already mentioned, the author being aware of the limitations due to noise, parasitic and tolerances, which might restrict the range of signal variation. However, the presented proof of concept shows how the subject of pattern formation could be associated not only to symmetric architectures but also to the design of what has been called a spatial comparator.

 

Author (s) Details

 

Liviu Goras
“Gheorghe Asachi” Technical University of Iasi, Romania and Institute of Computer Science, Romanian Academy, Iasi, Romania.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v8/4620